Around Hodge, Tate and Mumford-Tate conjectures on abelian
Around Hodge, Tate and Mumford-Tate conjectures on abelian varieties. Victoria Cantoral-Farfán. Advisor : Prof. Marc Hindry. Preliminaries. Definition.
A survey around the Hodge, Tate and Mumford-Tate conjectures for
Feb 26, 2016 ... A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties. Victoria Cantoral-Farfán. Abstract. We describe Hodge ...
ON THE TATE AND MUMFORD-TATE CONJECTURES IN
We prove the Tate conjecture for divisor classes and the Mumford-Tate ... abelian varieties, though it is known for K3 surfaces, again by André and Tankeev. ... number in the family and V is a variation of Hodge structure over S such that on a ...
A Survey of the Hodge Conjecture for Abelian Varieties
jecture for abelian varieties, with an emphasis on how Mumford-Tate groups have ... for example, the Hodge conjecture is true for simple abelian varieties of ...
C. Schnell TWO LECTURES ABOUT MUMFORD-TATE GROUPS
Hodge structure H. Roughly speaking, knowing the Mumford-Tate group of H is the same as knowing ... classes (for instance, the Hodge conjecture). 1.1. Hodge ... Clearly, S is an algebraic subgroup of GL2, defined over Q, and abelian. We have ..... set of Hodge classes can vary wildly as the point b moves around. On the ...
Recent Progress and Open Problems in Function - Mathematics
Tate conjectures and function field analog of Birch and Swinnerton-Dyer ... conjecture, p-divisible or Barsotti-Tate groups, Hodge-Tate decomposition, Tate .... Around the same time, Drinfeld, again unaware of Carlitz work, but using ideas ..... Tate proved the Tate conjecture for abelian varieties over finite fields basically .
SATO-TATE DISTRIBUTIONS Let E: y2 = x3 +Ax +B be an elliptic
but a rich theory and a precise set of conjectures has arisen around them ... then prove the Sato–Tate conjecture for CM elliptic curves and present Tate's ... abelian variety over a number field and state the generalized Sato–Tate ... relate the identity component of the Sato–Tate group to the Mumford–Tate and Hodge groups.
The Lindemann-Weierstrass theorem for semi-abelian varieties over
May 26, 2008 ... 2.2 Construction of the Mumford-Tate group . . . . . . . . . . . 11 ... theorem, which is a special case of the Schanuel conjecture: Conjecture 1. ... Mumford-Tate group of an abelian variety (or, more properly, of a Hodge structure), and ... around t with residue zero at P. The space of differential forms of. ∗Note that ...
Faltings's Proof of the Mordell Conjecture
Our plan is to try to understand Faltings's proof of the Mordell conjecture. ... 3.4 The Hodge line bundle ωA/S .... This was conjectured by Mordell around 1910, and was proved by Faltings around 1983. ... If A is an abelian variety of dimension g, and l is a prime, then the l-adic Tate ...... Example 3.17 (Deligne– Mumford).
SELECTED MATHEMATICAL REVIEWS MR0231827 (38 #155
Aug 26, 2015 ... not be a moduli variety for abelian varieties and so (b) cannot be used. Shimura ... Mumford's work on moduli varieties allows one to construct a canonical model ..... proved the Hodge-Tate conjecture with no condition on X. ..... morphism around a point (f,λ) it suffices to show that Xfs has dimension 1 at.
Mathematisches Forschungsinstitut Oberwolfach Arithmetic
Construction of abelian varieties with given monodromy . ..... Hodge filtration. .... germs of Λ-local systems around the origin admits a Hasse-Arf filtration, .... The Mumford-Tate conjecture implies a strong link between monodromy groups.
Néron-Severi groups under specialization - MIT Mathematics
p-adic analogue of the variational Hodge conjecture, and prove that this analogue .... Independently at around the same time, D. Masser [Mas96] used methods of ... Mumford-Tate group of a complex abelian variety, there exists an abelian ...
Introduction - University of Chicago
varieties of Hodge type that parameterize isogenies of abelian varieties with additional struc- ture. ... whose Mumford-Tate group is anisotropic modulo center. ... have also been used by the author to prove the Tate conjecture for K3 surfaces ; cf. ...... open disk of radius 1 around the K0-valued point y0 attached to u ↦→ 0.
Two lectures about Mumford-Tate groups - Seminario Matematico
Hodge structure H. Roughly speaking, the knowledge of the Mumford–Tate group of. H is the ... For example, the Hodge conjecture for arbitrary powers of an ... Clearly, S is an algebraic subgroup of GL2, defined over Q, and abelian. ..... we know that the set of Hodge classes can vary wildly as the point b moves around.
Abelian varieties over finite fields - Department of Mathematics at
For a simple abelian variety A over a finite field K = Fq the Weil conjecture ... TWO (Tate) For simple abelian varieties A, B defined over a finite field we have: A ∼ B ...... 1: Around. Grothendieck's Esquisse d'un programme. London Math. Soc. ... [ 44] D. Mumford – A note of Shimura's paper “Discontinuous groups and abelian ...
CV - Binghamton University
Jan 14, 2016 ... A purity theorem for abelian schemes, Michigan Math. J. 52 (2004) ... Projective integral models of Shimura varieties of Hodge type with compact factors, ... Some cases of the Mumford–Tate Conjecture and Shimura Varieties,.
Personal Data Vita - Peter Jossen
Diploma thesis title: Hodge–Zahlen und. K– ¨Aquivalenz ... part of the Mumford– Tate conjecture. Nov 2011 ... Title: Around the Hodge conjecture for complex tori.
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