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Albanese varieties with modulus and Hodge theory

Kazuya Kato, Henrik Russell (2012)

Annales de l’institut Fourier

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 = we give a Hodge theoretic description.

Algebraic tori as Nisnevich sheaves with transfers

Bruno Kahn (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We relate R -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.

Commutative algebraic groups and p-adic linear forms

Clemens Fuchs, Duc Hiep Pham (2015)

Acta Arithmetica

Let G be a commutative algebraic group defined over a number field K that is disjoint over K from a and satisfies the condition of semistability. Consider a linear form l on the Lie algebra of G with algebraic coefficients and an algebraic point u in a p-adic neighbourhood of the origin with the condition that l does not vanish at u. We give a lower bound for the p-adic absolute value of l(u) which depends up to an effectively computable constant only on the height of the linear form, the height...

Dimension algébrique de sous-groupes analytiques de variétés de groupe

Michel Waldschmidt (1975)

Annales de l'institut Fourier

Soient G une variété de groupe définie sur le corps Q des nombres algébriques, et φ : C n G C un sous-groupe à n paramètres de G , de dimension algébrique d . Nous nous proposons de majorer le rang (sur Z ) des sous-groupes Γ de C n dont l’image par φ est contenue dans le groupe G Q des points algébriques de G .E. Bombieri et S. Lang ont déjà obtenu de telles majorations, en supposant que les points de Γ sont très bien distribués : pour d n + 1 , on a n 2 + 3 n pour des variétés linéaires, et 2 n 2 + 4 n pour des variétés abéliennes .Nous...

Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups

Filling Bestvina, Alex Eskin, Kevin Wortman (2013)

Journal of the European Mathematical Society

We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux....

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