scholarly journals ON THE RESIDUE OF EISENSTEIN CLASSES OF SIEGEL VARIETIES

2017 ◽  
Vol 60 (3) ◽  
pp. 539-553
Author(s):  
FRANCESCO LEMMA
Keyword(s):  
Motivic Cohomology ◽  
Abelian Scheme ◽  
Arbitrary Genus ◽  
Direct Corollary

AbstractEisenstein classes of Siegel varieties are motivic cohomology classes defined as pull-backs by torsion sections of the polylogarithm prosheaf on the universal abelian scheme. By reduction to the Hilbert–Blumenthal case, we prove that the Betti realization of these classes on Siegel varieties of arbitrary genus have non-trivial residue on zero-dimensional strata of the Baily–Borel–Satake compactification. A direct corollary is the non-vanishing of a higher regulator map.

scholarly journals Mazur’s rational torsion result for pointless genus one curves: examples

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Arjan Dwarshuis ◽  
Majken Roelfszema ◽  
Jaap Top
Keyword(s):  
Algebraic Geometry ◽  
Elliptic Curves ◽  
Rational Point ◽  
Torsion Points ◽  
Arbitrary Genus ◽  
Mazur’S Theorem ◽  
Genus One

AbstractThis note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over $$\mathbb {Q}$$ Q in a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point. The main result is that explicit examples are provided of ‘pointless’ genus one curves over $$\mathbb {Q}$$ Q corresponding to the torsion orders 7, 8, 9, 10, 12 (and hence, all possibilities) occurring in Mazur’s theorem. In fact three distinct methods are proposed for constructing such examples, each involving different in our opinion quite nice ideas from the arithmetic of elliptic curves or from algebraic geometry.

Tadpole operator for minimal models on arbitrary genus Riemann surfaces

1990 ◽  
Vol 237 (3-4) ◽  
pp. 379-385 ◽  
Author(s):  
G. Cristofano ◽  
G. Maiella ◽  
R. Musto ◽  
F. Nicodemi
Keyword(s):  
Riemann Surfaces ◽  
Minimal Models ◽  
Arbitrary Genus

scholarly journals EPIDEMIC ENCEPHALITIS AND SIMPLE HERPES

1927 ◽  
Vol 8 (6) ◽  
pp. 713-726 ◽  
Author(s):  
Simon Flexner
Keyword(s):  
Guinea Pig ◽  
Past Experience ◽  
The State ◽  
Encephalitis Virus ◽  
Point Of View ◽  
Epidemic Encephalitis ◽  
Direct Corollary ◽  
The Subject ◽  
Positive Results ◽  
Epidemic Diseases

The purpose of this paper is to explain the state of our knowledge of the etiology of epidemic encephalitis, and especially to draw a line of demarcation between the established virus of simple herpes and the hypothetical virus of epidemic encephalitis. It had already been shown that the experimental observations on rabbits do no suffice to prove the identity of the herpes with the encephalitis virus. The discussion of the subject in this paper shows that identity cannot be postulated on the basis of the performed guinea pig experiments. Attention has been drawn to the significant fact that there is lack of harmony in the positive results of those investigators who believe that the incitants of epidemic encephalitis have been discovered. An attempt has been made to attribute some of the discrepancies reported by these investigators either to accidental and contaminating microbic agents, or to the uncovering of virulent agents preexisting in a latent state in the animals employed for inoculation, the existence of which was not previously known or suspected. Since past experience leads us to believe in a single incitant for widespread epidemic diseases, it is probable that, when certainly discovered, the microbe of epidemic encephalitis will prove to be simple and not multiple. The direct corollary to this point of view is that up to the present, the etiology of epidemic encephalitis has not been determined.

Motives and modules over motivic cohomology

2006 ◽  
Vol 342 (10) ◽  
pp. 751-754 ◽  
Author(s):  
Oliver Röndigs ◽  
Paul Arne Østvær
Keyword(s):  
Motivic Cohomology

scholarly journals Duality for the de Rham cohomology of an abelian scheme

1998 ◽  
Vol 48 (5) ◽  
pp. 1379-1393 ◽  
Author(s):  
Robert F. Coleman
Keyword(s):  
De Rham Cohomology ◽  
Abelian Scheme ◽  
De Rham

scholarly journals Néron models and limits of Abel–Jacobi mappings

2010 ◽  
Vol 146 (2) ◽  
pp. 288-366 ◽  
Author(s):  
Mark Green ◽  
Phillip Griffiths ◽  
Matt Kerr
Keyword(s):  
Normal Function ◽  
Motivic Cohomology ◽  
Normal Functions ◽  
Geometric Setting ◽  
Neron Models ◽  
A Finite Group ◽  
Intermediate Jacobian ◽  
Néron Models ◽  
Singular Fibre ◽  
Finite Singularity

AbstractWe show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on motivic cohomology of the singular fibre, hence via regulators onK-groups of its substrata. Two examples are worked out in detail, for families of 1-cycles on CY and abelian 3-folds, where this produces interesting arithmetic constraints on such limits. We also show how to compute the finite ‘singularity group’ in the geometric setting.

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 Rost nilpotence and étale motivic cohomology

2018 ◽  
Vol 330 ◽  
pp. 420-432 ◽  
Author(s):  
Andreas Rosenschon ◽  
Anand Sawant
Keyword(s):  
Motivic Cohomology

An Overview of the Proof

2019 ◽  
pp. 3-22
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Motivic Cohomology ◽  
Norm Residue ◽  
Cohomology Operations ◽  
Definition Of ◽  
Special Case

This chapter provides the main steps in the proof of Theorems A and B regarding the norm residue homomorphism. It also proves several equivalent (but more technical) assertions in order to prove the theorems in question. This chapter also supplements its approach by defining the Beilinson–Lichtenbaum condition. It thus begins with the first reductions, the first of which is a special case of the transfer argument. From there, the chapter presents the proof that the norm residue is an isomorphism. The definition of norm varieties and Rost varieties are also given some attention. The chapter also constructs a simplicial scheme and introduces some features of its cohomology. To conclude, the chapter discusses another fundamental tool—motivic cohomology operations—as well as some historical notes.

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