scholarly journals Structure de poids à la Bondarko sur les motifs de Beilinson

2011 ◽  
Vol 147 (5) ◽  
pp. 1447-1462 ◽  
Author(s):  
David Hébert
Keyword(s):  
Finite Type ◽  
Base Scheme ◽  
Weight Structure

AbstractBondarko defines and studies the notion of weight structure and he shows that there exists a weight structure over the category of Voevodsky motives with rational coefficients (over a field of characteristic 0). In this paper we extend this weight structure to the category of Beilinson motives (for any scheme of finite type over a base scheme which is excellent of dimension at most two) introduced and studied by Cisinsky and Déglise. We also check the weight exactness of the Grothendieck operations.

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 NON-COMMUTATIVE LOCALIZATIONS OF ADDITIVE CATEGORIES AND WEIGHT STRUCTURES

2016 ◽  
Vol 17 (4) ◽  
pp. 785-821 ◽  
Author(s):  
Mikhail V. Bondarko ◽  
Vladimir A. Sosnilo
Keyword(s):  
Triangulated Category ◽  
Perfect Field ◽  
Efficient Tool ◽  
Direct Sums ◽  
Base Scheme ◽  
General Base ◽  
Additive Category ◽  
Weight Structure ◽  
W Prime ◽  
Weight Structures

In this paper we demonstrate thatnon-commutative localizationsof arbitrary additive categories (generalizing those defined by Cohn in the setting of rings) are closely (and naturally) related to weight structures. Localizing an arbitrary triangulated category$\text{}\underline{C}$by a set$S$of morphisms in the heart$\text{}\underline{Hw}$of a weight structure$w$on it one obtains a triangulated category endowed with a weight structure$w^{\prime }$. The heart of$w^{\prime }$is a certain version of the Karoubi envelope of the non-commutative localization$\text{}\underline{Hw}[S^{-1}]_{\mathit{add}}$(of$\text{}\underline{Hw}$by$S$). The functor$\text{}\underline{Hw}\rightarrow \text{}\underline{Hw}[S^{-1}]_{\mathit{add}}$is the natural categorical version of Cohn’s localization of a ring, i.e., it is universal among additive functors that make all elements of$S$invertible. For any additive category$\text{}\underline{A}$, taking$\text{}\underline{C}=K^{b}(\text{}\underline{A})$we obtain a very efficient tool for computing$\text{}\underline{A}[S^{-1}]_{\mathit{add}}$; using it, we generalize the calculations of Gerasimov and Malcolmson (made for rings only). We also prove that$\text{}\underline{A}[S^{-1}]_{\mathit{add}}$coincides with the ‘abstract’ localization$\text{}\underline{A}[S^{-1}]$(as constructed by Gabriel and Zisman) if$S$contains all identity morphisms of$\text{}\underline{A}$and is closed with respect to direct sums. We apply our results to certain categories of birational motives$DM_{gm}^{o}(U)$(generalizing those defined by Kahn and Sujatha). We define$DM_{gm}^{o}(U)$for an arbitrary$U$as a certain localization of$K^{b}(Cor(U))$and obtain a weight structure for it. When$U$is the spectrum of a perfect field, the weight structure obtained this way is compatible with the corresponding Chow and Gersten weight structures defined by the first author in previous papers. For a general$U$the result is completely new. The existence of the correspondingadjacent$t$-structure is also a new result over a general base scheme; its heart is a certain category of birational sheaves with transfers over$U$.

scholarly journals Oriented bivariant theory, II: Algebraic cobordism of S-schemes

2019 ◽  
Vol 30 (06) ◽  
pp. 1950031
Author(s):  
Shoji Yokura
Keyword(s):  
Finite Type ◽  
Double Point ◽  
Base Field ◽  
Base Scheme ◽  
Bivariant Theory ◽  
Algebraic Cobordism

This is a sequel to our previous paper “Oriented bivariant theory, I”. In 2001, Levine and Morel constructed algebraic cobordism for (reduced) schemes [Formula: see text] of finite type over a base field [Formula: see text] in an abstract way and later Levine and Pandharipande reconstructed it more geometrically, using “double point degeneration”. In this paper in a similar manner to the construction of Levine–Morel, we construct an algebraic cobordism for a scheme [Formula: see text] over a fixed scheme [Formula: see text] in such a way that if the target scheme [Formula: see text] is the point [Formula: see text], then our algebraic cobordism is isomorphic to Levine–Morel’s algebraic cobordism. Our algebraic cobordism can be interpreted as “a family of algebraic cobordism” parametrized by the base scheme [Formula: see text].

scholarly journals Recent Progress on Submersions: A Survey and New Properties

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Gabriel Picavet
Keyword(s):  
Finite Type ◽  
Recent Progress ◽  
Valuation Domain ◽  
Base Scheme ◽  
Dominant Property ◽  
Dual Notion

This paper is a survey about recent progress on submersive morphisms of schemes combined with new results that we prove. They concern the class of quasicompact universally subtrusive morphisms that we introduced about 30 years ago. They are revisited in a recent paper by Rydh, with substantial complements and key results. We use them to show Artin-Tate-like results about the 14th problem of Hilbert, for a base scheme either Noetherian or the spectrum of a valuation domain. We look at faithfully flat morphisms and get “almost” Artin-Tate-like results by considering the Goldman (finite type) points of a scheme. Bjorn Poonen recently proved that universally closed morphisms are quasicompact. By introducing incomparable morphisms of schemes, we are able to characterize universally closed surjective morphisms that are either integral or finite. Next we consider pure morphisms of schemes introduced by Mesablishvili. In the quasicompact case, they are universally schematically dominant morphisms. This leads us to a characterization of universally subtrusive morphisms by purity. Some results on the schematically dominant property are given. The paper ends with properties of monomorphisms and topological immersions, a dual notion of submersions.

scholarly journals Connective Algebraic K-theory

2014 ◽  
Vol 13 (1) ◽  
pp. 9-56 ◽  
Author(s):  
Shouxin Dai ◽  
Marc Levine
Keyword(s):  
Finite Type ◽  
Formal Group ◽  
Abelian Category ◽  
Homology Theory ◽  
Fundamental Class ◽  
Coherent Sheaves ◽  
Base Scheme ◽  
Stable Homotopy Category ◽  
Algebraic Cobordism ◽  
Coefficient Ring

AbstractWe examine the theory of connective algebraic K-theory, , defined by taking the −1 connective cover of algebraic K-theory with respect to Voevodsky's slice tower in the motivic stable homotopy category. We extend to a bi-graded oriented duality theory when the base scheme is the spectrum of a field k of characteristic zero. The homology theory may be viewed as connective algebraic G-theory. We identify for X a finite type k-scheme with the image of in , where is the abelian category of coherent sheaves on X with support in dimension at most n; this agrees with the (2n,n) part of the theory of connective algebraic K-theory defined by Cai. We also show that the classifying map from algebraic cobordism identifies with the universal oriented Borel-Moore homology theory having formal group law u + υ − βuυ with coefficient ring ℤ[β]. As an application, we show that every pure dimension d finite type k-scheme has a well-defined fundamental class [X]CK in ΩdCK(X), and this fundamental class is functorial with respect to pull-back for l.c.i. morphisms.

STRUKTUR KOMPLEKS DALAM BAHASA INDONESIA ILMIAH DAN MASALAH PENERJEMAHANNYA KE DALAM BAHASA INGGRIS

2018 ◽  
Vol 17 (1) ◽  
Author(s):  
Ni Ketut Mirahayuni ◽  
Susie Chrismalia Garnida ◽  
Mateus Rudi Supsiadji
Keyword(s):  
Complex Structure ◽  
General Concept ◽  
Target Language ◽  
Complex Structures ◽  
Scientific Language ◽  
Logical Relation ◽  
Information Packaging ◽  
Weight Structure ◽  
The Difference ◽  
Target Languages

Abstract. Translating complex structures have always been a challenge for a translator since the structures can be densed with ideas and particular logical relations. The purpose of translation is reproducing texts into another language to make them available to wider readerships. Since language is not merely classification of a set of universal and general concept, that each language articulates or organizes the world differently, the concepts in one language can be radically different from another. One issue in translation is the difference among languages, that the wider gaps between the source and target languages may bring greater problems of transfer of message from the source into the target languages (Culler, 1976). Problematic factors involved in translation include meaning, style, proverbs, idioms and others. A number of translation procedures and strategies have been discussed to solve translation problems. This article presents analysis of complex structures in scientific Indonesian, the problems and effects on translation into English. The study involves data taken from two research article papers in Indonesian to be translated into English. The results of the analysis show seven (7) problems of Indonesian complex structures, whose effect on translation process can be grouped into two: complex structures related to grammar (including: complex structure with incomplete information, run-on sentences, redundancy , sentence elements with inequal semantic relation, and logical relation and choice of conjunctor) and complex structures related to information processing in discourse (including: front-weight- structure and thematic structure with changes of Theme element). Problems related to grammar may be solved with language economy and accuracy while those related to discourse may be solved with understanding information packaging patterns in the target language discourse. Keywords: scientific language, complex structures, translation

scholarly journals Co-Treatment of Purified Annatto Oil (Bixa orellana L.) and Its Granules (Chronic®) Improves the Blood Lipid Profile and Bone Protective Effects of Testosterone in the Orchiectomy-Induced Osteoporosis in Wistar Rats

Molecules ◽  
2021 ◽  
Vol 26 (16) ◽  
pp. 4720
Author(s):  
Arlindo César Matias Pereira ◽  
Helison de Oliveira Carvalho ◽  
Danna Emanuelle Santos Gonçalves ◽  
Karyny Roberta Tavares Picanço ◽  
Abrahão Victor Tavares de Lima Teixeira dos dos Santos ◽  
...  
Keyword(s):  
Lipid Profile ◽  
Wistar Rats ◽  
Calcium Concentration ◽  
Calcium Content ◽  
Blood Lipid ◽  
Atomic Absorption Spectrophotometry ◽  
Protective Effects ◽  
Blood Lipid Profile ◽  
Bone Calcium ◽  
Weight Structure

This study aimed to evaluate and compare the effects of co-treatment with purified annatto oil (PAO) or its granules (GRA, Chronic®) with that of testosterone on the orchiectomy-induced osteoporosis in Wistar rats. After surgery, rats were treated from day 7 until day 45 with testosterone only (TES, 7 mg/kg, IM) or TES + PAO or GRA (200 mg/kg, p.o.). The following parameters were evaluated: food/water intake, weight, HDL, LDL, glucose, triglycerides (TG), total cholesterol (TC), alkaline phosphatase levels, blood phosphorus and calcium contents, femur weight, structure (through scanning electron microscopy), and calcium content (through atomic absorption spectrophotometry). Our results show that orchiectomy could significantly change the blood lipid profile and decrease bone integrity parameters. Testosterone reposition alone could improve some endpoints, including LDL, TC, bone weight, and bone calcium concentration. However, other parameters were not significantly improved. Co-treatment with PAO or GRA improved the blood lipid profile and bone integrity more significantly and improved some endpoints not affected by testosterone reposition alone (such as TG levels and trabeculae sizes). The results suggest that co-treatment with annatto products improved the blood lipid profile and the anti-osteoporosis effects of testosterone. Overall, GRA had better results than PAO.

scholarly journals Improvement on Load-Induced Cascading Failure in Asymmetrical Interdependent Networks: Modeling and Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Haiyan Han ◽  
Rennong Yang
Keyword(s):  
Load Capacity ◽  
Small World ◽  
Cascading Failure ◽  
Modeling And Analysis ◽  
Interdependent Networks ◽  
Interdependent Network ◽  
Capacity Model ◽  
Weight Structure ◽  
Edge Failure ◽  
Asymmetrical Model

Many real-world systems can be depicted as interdependent networks and they usually show an obvious property of asymmetry. Furthermore, node or edge failure can trigger load redistribution which leads to a cascade of failure in the whole network. In order to deeply investigate the load-induced cascading failure, firstly, an asymmetrical model of interdependent network consisting of a hierarchical weighted network and a WS small-world network is constructed. Secondly, an improved “load-capacity” model is applied for node failure and edge failure, respectively, followed by a series of simulations of cascading failure over networks in both interdependent and isolated statuses. The simulation results prove that the robustness in isolated network changes more promptly than that in the interdependent one. Network robustness is positively related to “capacity,” but negatively related to “load.” The hierarchical weight structure in the subnetwork leads to a “plateau” phenomenon in the progress of cascading failure.

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