Existence of discrete cocompact subgroups of reductive groups over local fields.
Existence of rational points on smooth projective varieties
Explicit descriptions of quadratic maps on ℙ¹ defined over a field K
Explicit global function fields over the binary field with many rational places
Explicit -descent for elliptic curves in characteristic
Explicit p-adic theta function.
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...
Exponential sums on (Gm)n.
Extension of Estermann’s theorem to Euler products associated to a multivariate polynomial
Given a multivariate polynomial with integral coefficients verifying an hypothesis of analytic regularity (and satisfying ), we determine the maximal domain of meromorphy of the Euler product and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.
Extension universelle d'une variété abélienne et hauteurs des points de torsion
Extensions of Abelian Varieties Defined Over a Finite Field.
Extensions with restricted ramification and duality for arithmetic schemes
Extremal rational elliptic surfaces in characteristic p. I. Beauville surfaces.