scholarly journals Weight structures vs.t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)

2010 ◽  
Vol 6 (3) ◽  
pp. 387-504 ◽  
Author(s):  
M.V. Bondarko
Keyword(s):  
Preceding Paper ◽  
Spectral Sequences ◽  
Motivic Cohomology ◽  
Adjacent Structures ◽  
Unramified Cohomology ◽  
Homological Functor ◽  
Stable Homotopy Category ◽  
Weight Structure ◽  
The One ◽  
Weight Structures

AbstractIn this paper we introduce a new notion ofweight structure (w)for a triangulated categoryC; this notion is an important natural counterpart of the notion oft-structure. It allows extending several results of the preceding paper [Bon09] to a large class of triangulated categories and functors.Theheartofwis an additive categoryHw⊂C. We prove that a weight structure yields Postnikov towers for anyX∈ObjC(whose 'factors'Xi∈ObjHw). For any (co)homological functorH:C→A(Ais abelian) such a tower yields aweight spectral sequenceT : H(Xi[j]) ⇒H(X[i + j]); Tis canonical and functorial inXstarting fromE2.Tspecializes to the usual (Deligne) weight spectral sequences for 'classical' realizations of Voevodsky's motivesDMeffgm(if we considerw = wChowwithHw=Choweff) and to Atiyah-Hirzebruch spectral sequences in topology.We prove that there often exists an exact conservative weight complex functorC→K(Hw). This is a generalization of the functort:DMeffgm→Kb(Choweff) constructed in [Bon09] (which is an extension of the weight complex of Gillet and Soulé). We prove thatK0(C) ≅K0(Hw) under certain restrictions.We also introduce the concept of adjacent structures: at-structure isadjacenttowif their negative parts coincide. This is the case for the Postnikovt-structure for the stable homotopy categorySH(of topological spectra) and a certain weight structure for it that corresponds to the cellular filtration. We also define a new (Chow)t-structuretChowforDMeff_⊃DMeffgmwhich is adjacent to the Chow weight structure. We haveHtChow≅ AddFun(Choweffop,Ab);tChowis related to unramified cohomology. Functors left adjoint to those that aret-exact with respect to somet-structures are weight-exact with respect to the corresponding adjacent weight structures, and vice versa. Adjacent structures identify two spectral sequences converging toC(X,Y): the one that comes from weight truncations ofXwith the one coming fromt-truncations ofY(forX,Y∈ObjC). Moreover, the philosophy of adjacent structures allows expressing torsion motivic cohomology of certain motives in terms of the étale cohomology of their 'submotives'. This is an extension of the calculation of E2of coniveau spectral sequences (by Bloch and Ogus).

scholarly journals ℤ[1/p]-motivic resolution of singularities

2011 ◽  
Vol 147 (5) ◽  
pp. 1434-1446 ◽  
Author(s):  
M. V. Bondarko
Keyword(s):  
Preceding Paper ◽  
Resolution Of Singularities ◽  
Cohomology Theory ◽  
Spectral Sequences ◽  
Perfect Field ◽  
Chow Motives ◽  
Unramified Cohomology ◽  
Weight Structure ◽  
Weight Structures

AbstractThe main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with ℤ[1/p]-coefficients over a perfect field k of characteristic p generate the category DMeffgm[1/p] (of effective geometric Voevodsky’s motives with ℤ[1/p]-coefficients). It follows that DMeffgm[1/p] can be endowed with a Chow weight structure wChow whose heart is Choweff[1/p] (weight structures were introduced in a preceding paper, where the existence of wChow for DMeffgmℚ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor DMeffgm[1/p]→Kb (Choweff [1/p]) (which induces an isomorphism on K0-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on DMeffgm[1/p] . We also mention a certain Chow t-structure for DMeff−[1/p] and relate it with unramified cohomology.

scholarly journals Chow motives without projectivity

2009 ◽  
Vol 145 (5) ◽  
pp. 1196-1226 ◽  
Author(s):  
Jörg Wildeshaus
Keyword(s):  
Shimura Varieties ◽  
Spectral Sequences ◽  
Perfect Field ◽  
Basic Properties ◽  
Structure Building ◽  
Princeton University ◽  
Chow Motives ◽  
Weight Structure ◽  
Compositio Math ◽  
Weight Structures

AbstractIn a recent paper, Bondarko [Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general), Preprint (2007), 0704.4003] defined the notion of weight structure, and proved that the category DMgm(k) of geometrical motives over a perfect field k, as defined and studied by Voevodsky, Suslin and Friedlander [Cycles, transfers, and motivic homology theories, Annals of Mathematics Studies, vol. 143 (Princeton University Press, Princeton, NJ, 2000)], is canonically equipped with such a structure. Building on this result, and under a condition on the weights avoided by the boundary motive [J. Wildeshaus, The boundary motive: definition and basic properties, Compositio Math. 142 (2006), 631–656], we describe a method to construct intrinsically in DMgm(k) a motivic version of interior cohomology of smooth, but possibly non-projective schemes. In a sequel to this work [J. Wildeshaus, On the interior motive of certain Shimura varieties: the case of Hilbert–Blumenthal varieties, Preprint (2009), 0906.4239], this method will be applied to Shimura varieties.

CONFINEMENT OF QUARKS AND GLUONS II

1995 ◽  
Vol 10 (22) ◽  
pp. 3155-3167 ◽  
Author(s):  
KAZUHIKO NISHIJIMA
Keyword(s):  
Quantum Chromodynamics ◽  
Preceding Paper ◽  
Asymptotic Freedom ◽  
Color Confinement ◽  
The One

It is shown that color confinement is a consequence of BRS invariance and asymptotic freedom of quantum chromodynamics. BRS invariance is exploited to define color confinement, and asymptotic freedom is utilized to prove it. The proof presented in this paper is an extension of the one in the preceding paper.

Motivic cohomology of quadrics and the coniveau spectral sequence

2010 ◽  
Vol 6 (3) ◽  
pp. 547-589 ◽  
Author(s):  
Nobuaki Yagita
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Motivic Cohomology

AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term

scholarly journals Experimental researches in electricity: Twelfth series

1843 ◽  
Vol 4 ◽  
pp. 49-52
Keyword(s):  
Electric Discharge ◽  
Physical State ◽  
Charged Particles ◽  
Preceding Paper ◽  
The Other ◽  
Electric Conduction ◽  
The One ◽  
Experimental Researches ◽  
Inductive Charge ◽  
Perfect Conduction

The object of the present series of researches is to examine how far the principal general facts in electricity are explicable on the theory adopted by the author, and detailed in his last memoir, re­lative to the nature of inductive action. The operation of a body charged with electricity, of either the positive or negative kind, on other bodies in its vicinity, as long as it retains the whole of its charge, may be regarded as simple induction , in contradistinction to the effects which follow the destruction of this statical equilibrium, and imply a transit of the electrical forces from the charged body to those at a distance, and which comprehend the phenomena of the electric discharge . Having considered, in the preceding paper, the process by which the former condition is established, and which consists in the successive polarization of series of contiguous particles of the interposed insulating dielectric; the author here proceeds to trace the process, which, taking place consequently on simple induction, terminates in that sudden, and often violent interchange of electric forces constituting disruption , or the electric discharge. He investigates, by the application of his theory, the gradual steps of transition which may be traced between perfect insulation on the one hand, and perfect conduction on the other, derived from the varied degrees of specific electric relations subsisting among the particular substances interposed in the circuit: and from this train of reasoning he deduces the conclusion that induction and conduction not only depend essentially on the same principles, but that they may be regarded as being of the same nature, and as differing merely in degree. The fact ascertained by Professor Wheatstone, that electric conduction, even in the most perfect conductors, as the metals, requires for its completion a certain appreciable time, is adduced in corrobo­ration of these views; for any retardation, however small, in the transmission of electric forces can result only from induction; the degree of retardation, and, of course, the time employed, being proportional to the capacity of the particles of the conducting body for retaining a given intensity of inductive charge. The more perfect insulators, as lac, glass and sulphur, are capable of retaining electri­city of high intensity; while, on the contrary, the metals and other excellent conductors, possess no power of retention when the in­tensity of the charge exceeds the lowest degrees. It would appear, however, that gases possess a power of perfect insulation, and that the effects generally referred to their capacity of conduction, are only the results of the carrying power of the charged particles either of the gas, or of minute particles of dust which may be present in them: and they perhaps owe their character of perfect insulators to their peculiar physical state, and to the condition of separation under which their particles are placed. The changes produced by heat on the conducting power of different bodies is not uniform; for in some, as sulphuret of silver and fluoride of lead, it is increased; while in others, as in the metals and the gases, it is diminished by an augmentation of temperature.

scholarly journals Cell interactions between histoincompatible T and B lymphocytes. VII. Cooperative responses between lymphocytes are controlled by genes in the I region of the H-2 complex

1975 ◽  
Vol 141 (1) ◽  
pp. 263-268 ◽  
Author(s):  
DH Katz ◽  
M Graves ◽  
ME Dorf ◽  
H Dimuzio ◽  
B Benacerraf
Keyword(s):  
B Lymphocytes ◽  
Preceding Paper ◽  
Gene Complex ◽  
Compelling Evidence ◽  
T And B Cells ◽  
Cooperative Interactions ◽  
The One ◽  
Or Genes ◽  
Relevant Gene

The results of this study provide compelling evidence for the existence of the gene or genes controlling optimal T-B-cell cooperative interactions in the designated I region of the H-2 gene complex. Previously, we have speculated that the relevant gene(s) involved may well be located in this region based on several observations from our earlier work in this area (3, 5, 6). Thus, in the preceding paper, we showed that T and B cells from B10.BR and A strain mice developed effective cooperative interactions in vitro to DNP-KLH in a system identical to the one reported herein. Since these mice differ for genes in the S and D regions of H-2 but are identical for K and I region genes, we were able to localize the critical genes to the K-end of H-2.

scholarly journals Mixed motivic sheaves (and weights for them) exist if ‘ordinary’ mixed motives do

2015 ◽  
Vol 151 (5) ◽  
pp. 917-956 ◽  
Author(s):  
Mikhail V. Bondarko
Keyword(s):  
Finite Type ◽  
Main Tool ◽  
Decomposition Theorem ◽  
Weight Filtration ◽  
Closed Fields ◽  
Weight Structure ◽  
Residue Fields ◽  
Algebraically Closed Fields ◽  
Mixed Motives ◽  
Weight Structures

The goal of this paper is to prove that if certain ‘standard’ conjectures on motives over algebraically closed fields hold, then over any ‘reasonable’ scheme $S$ there exists a motivic$t$-structure for the category $\text{DM}_{c}(S)$ of relative Voevodsky’s motives (to be more precise, for the Beilinson motives described by Cisinski and Deglise). If $S$ is of finite type over a field, then the heart of this $t$-structure (the category of mixed motivic sheaves over $S$) is endowed with a weight filtration with semisimple factors. We also prove a certain ‘motivic decomposition theorem’ (assuming the conjectures mentioned) and characterize semisimple motivic sheaves over $S$ in terms of those over its residue fields. Our main tool is the theory of weight structures. We actually prove somewhat more than the existence of a weight filtration for mixed motivic sheaves: we prove that the motivic $t$-structure is transversal to the Chow weight structure for $\text{DM}_{c}(S)$ (that was introduced previously by Hébert and the author). We also deduce several properties of mixed motivic sheaves from this fact. Our reasoning relies on the degeneration of Chow weight spectral sequences for ‘perverse étale homology’ (which we prove unconditionally); this statement also yields the existence of the Chow weight filtration for such (co)homology that is strictly restricted by (‘motivic’) morphisms.

scholarly journals Zur spontanen Magnetisierung dünner ferromagnetischer Schichten

1964 ◽  
Vol 19 (13) ◽  
pp. 1580-1591
Author(s):  
Rainer J. Jelitto
Keyword(s):  
Thin Films ◽  
Digital Computer ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Preceding Paper ◽  
Cubic Lattice ◽  
Compact Material ◽  
Ferromagnetic Films ◽  
Special Lattice ◽  
The One

In a preceding paper (I) the spectra of the one-spinwave-eigenstates of an ideal HEISENBERG-model for thin ferromagnetic films were derived for a special type of surface-orientations.Now these results are applied to the cubic lattice types. First a theory is given for the calculation of certain coefficients by which the general equations of (I) are related to the special lattice types and surface orientations. It is shown that some of the most important orientations of the cubic lattice types belong to the case treated in (I).For these orientations the dependence of the spontaneous magnetization on temperature and thickness of the film is calculated from the spinwave spectra. The formula obtained for this function was evaluated on a digital computer. The results, some of which are plotted, are discussed and compared with experimental dates.In all cases the deviations from the magnetization of the compact material are found to be small, down to very thin films.

scholarly journals The mechanism of chemical change. Part II.—Catalysis of the mutarotation of beryllium benzoylcamphor

1931 ◽  
Vol 132 (820) ◽  
pp. 398-415 ◽  
Keyword(s):  
Hydrogen Atom ◽  
Chemical Change ◽  
Preceding Paper ◽  
Internal Electrolysis ◽  
Mobile Hydrogen ◽  
Acid And Base ◽  
Alternative Position ◽  
The One ◽  
Single Bonds ◽  
Mobile Hydrogen Atom

The preceding paper of this series on “Promotion and Arrest of Mutarotation of Tetra-acetylglucose in Ethyl Acetate” described the most successful experiments that have yet been made with a view to controlling the facile isomeric changes which depend on the migration of a hydrogen atom with a concurrent re-arrangement of bonds in the molecule of an unsaturated (or cyclic) organic compound. These “desmotropic” or “prototropic" changes proceed normally only in presence of an amphoteric solvent, such as water or a mixture of pyridine and cresol, which is able simultaneously to remove a proton from one position in the molecule, and to supply a proton in the alternative position. The re-arrangement of single and double bonds, which accompanies the migration of the hydrogen atom, provides a conducting mechanism whereby an electron can be transferred through the intermediate conjugated system from one point of attachment of the mobile hydrogen atom to the other. This electronic migration makes it possible to neutralise the negative charge produced by the removal of a proton from the one point of attachment, together with the positive charge produced by the addition of a proton to the second point of attachment, so that the mobile hydrogen atom need not carry its electron with it, but can migrate in the form of an ion. The mechanism of the prototropic change can then be represented as a sort of internal electrolysis in which the acid and base act as negative and positive poles, whilst the conjugated double and single bonds of the organic molecule take the place of the electrolyte. Thus, if we represent the acid and base as HA and B, and the two forms of the prototropic compound as HS and SH, the reversible isomeric change can be represented by the following scheme: B + HS + HA ⇌ + BH + SH + A̅. In this scheme the arrows show the direction in which the electron migrates through the molecule as a result of the bond-shifting, whilst the proton migrates in the same direction through the medium . Apart from the prototropic change, the action formulated above is a simple reversible neutralisation of an acid and base, which, if the prototropic compounds were eliminated, could be represented by the equation B + HA ⇌ + BH + A̅, e. g. , NH 3 + HAc ⇌ + NH + A̅c.

scholarly journals Refractive dispersion of organic compounds. V-Oxygenated derivatives of cyclohexane the inadequacy of the Ketteler-Helmholtz equation

1934 ◽  
Vol 146 (857) ◽  
pp. 300-312 ◽  
Keyword(s):  
Double Bond ◽  
Preceding Paper ◽  
Hydroxyl Group ◽  
Double Bonds ◽  
Ring Compounds ◽  
Wide Range ◽  
Olefinic Double Bond ◽  
The One ◽  
Conjugated Compounds ◽  
Derivatives Of

In the preceding paper of this series, refractive indices and molecular extinction coefficients over a wide range of wave-lengths were recorded for the two cyclic hydrocarbons cyclohexene and 1:3- cyclohexadiene . These observations completed a study of the refractive dispersions of the series of 6-ring compounds C 6 H 12 , C 6 H 10 , C 6 H 8 , C 6 H 6 ; they also provided a basis for the study of the phenomenon of "optical exaltation," which is exhibited by compounds containing conjugated double bonds, since the last two members of the series belong to this type. Conjugation, however, may be effected, not only between two olefinic double bonds, but also between an olefinic double bond and an oxygenated radical, such as the carboxyl, carbonyl, or hydroxyl group. The present paper, therefore, records the absorption spectra and refractive dispersions of three oxygenated derivated of cyclohexane, namely, cyclohexanol , cyclohexanone , and ethyl hexahydrobenzoate , in the molecules of which each of the preceding groups is exemplified. Dispersion curves are thus now available for typical compounds of the cyclohexane series containing "unsaturated" radicals of all the principal types which are used in constructing conjugated systems, and the way has been prepared for a detailed study of conjugation, as exemplified on the one hand by cyclo hexadiene, and similar compounds containing two olefinic radicals, and on the other hand by a variety of compounds containing a double bond in addition to a hydroxyl, carbonyl, or carboxyl group. It is anticipated that, with the help of the date set out in the preceding and present papers, it will be possible in a later communication to demonstrate in what respect the behaviour of conjugated compounds differs from that which might be anticipated from a merely additive behaviour of the chromophoric radicals, and thus to determine the nature, and if possible to discover the origin, of the phenomenon of optical exaltation.

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