Explicit determination of the images of the Galois representations attached to abelian surfaces with .
Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
1. Motivation. Let J₀(N) denote the Jacobian of the modular curve X₀(N) parametrizing pairs of N-isogenous elliptic curves. The simple factors of J₀(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dim A. We shall sometimes abbreviate "real multiplication" to "RM" and say that A has maximal RM by the totally real field F if A has an action of the full ring of integers of F. We say that a...
Explicit Selmer groups for cyclic covers of ℙ¹
For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group is a subgroup of the Galois cohomology group , defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the ‘fake Selmer group’, whose definition is more amenable to explicit computations. In this paper we define in the same setting the ‘explicit Selmer group’, which is isomorphic...
Facteurs -simples de de grande dimension et de grand rang
Factorization estimates for abelian varieties
Finiteness theorems for torsion of abelian varieties over large algebraic fields
Fonctions automorphes et variétés abéliennes
Fonctions thêta et points de torsion des variétés abéliennes
Formes linéaires de logarithmes effectives sur les variétés abéliennes
Fourier-Mukai partners of canonical covers of bielliptic and Enriques surfaces
Galois descent and twists of an abelian variety
Generalized Jacobi forms and abelian schemes over arithmetic varieties.
We generalize Jacobi forms of an arbitrary degree and construct torus bundles over abelian schemes whose sections can be identified with such generalized Jacobi forms.
Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of -kernel.
Geometrical model theory.
H. L. M. (Hrushovski-Lang-Mordell)
Height pairings for algebraic cycles on abelian varieties
Horizontal Factorizations of Certain Hasse-Weil Zeta Functions - a Remark on a Paper by Taniyama
Il n'y a pas de variété abélienne sur Z.
Implementing 2-descent for Jacobians of hyperelliptic curves
Inégalité de Vojta en dimension supérieure