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.
Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures)
?-factor of a tamely ramified sheaf on a variety.
Failure of the Hasse principle for Châtelet surfaces in characteristic
Given any global field of characteristic , we construct a Châtelet surface over that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic , thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
Faisceaux pervers, transformation de Mellin et déterminants
Fake CM and the stable model of .
Faltings modular height and self-intersection of dualizing sheaf.
Families of hypersurfaces of large degree
Grauert and Manin showed that a non-isotrivial family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.
Families of Mumford curves