Displaying similar documents to “Integral canonical models of Shimura varieties”

The period-index problem in WC-groups IV: a local transition theorem

Pete L. Clark (2010)

Journal de Théorie des Nombres de Bordeaux

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Let K be a complete discretely valued field with perfect residue field k . Assuming upper bounds on the relation between period and index for WC-groups over k , we deduce corresponding upper bounds on the relation between period and index for WC-groups over K . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of of torsors under abelian varieties with good reduction and...

The Tate pairing for Abelian varieties over finite fields

Peter Bruin (2011)

Journal de Théorie des Nombres de Bordeaux

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In this expository note, we describe an arithmetic pairing associated to an isogeny between Abelian varieties over a finite field. We show that it generalises the Frey–Rück pairing, thereby giving a short proof of the perfectness of the latter.

The Mordell–Lang question for endomorphisms of semiabelian varieties

Dragos Ghioca, Thomas Tucker, Michael E. Zieve (2011)

Journal de Théorie des Nombres de Bordeaux

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The Mordell–Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of images of the origin under a finitely generated semigroup of translations. We study the analogous question in which the translations are replaced by algebraic group endomorphisms (and the origin is replaced by another point). We show that the conclusion...

Albanese varieties with modulus and Hodge theory

Kazuya Kato, Henrik Russell (2012)

Annales de l’institut Fourier

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Let X be a proper smooth variety over a field k of characteristic 0 and Y an effective divisor on X with multiplicity. We introduce a generalized Albanese variety Alb ( X , Y ) of X of modulus Y , as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For k = ℂ we give a Hodge theoretic description.

Quotients of toric varieties by actions of subtori

Joanna Święcicka (1999)

Colloquium Mathematicae

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Let X be an algebraic toric variety with respect to an action of an algebraic torus S. Let Σ be the corresponding fan. The aim of this paper is to investigate open subsets of X with a good quotient by the (induced) action of a subtorus T ⊂ S. It turns out that it is enough to consider open S-invariant subsets of X with a good quotient by T. These subsets can be described by subfans of Σ. We give a description of such subfans and also a description of fans corresponding to quotient varieties....