On Values of Zeta Functions and ?-adic Euler Characteristc.
On Zariski's theorem in positive characteristic
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...
Operateurs differentiels de Shimura et espaces prehomogenes.
Optimal levels for modular mod 2 representations over totally real fields.
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.
Ordinariness in good reductions of Shimura varieties of PEL-type
Ordinary reduction of K3 surfaces
Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.
Ouverts analytiques d'une courbe algébrique en géométrie rigide
Ouverts analytiques d'une courbe algébrique en géométrie rigide
Nous étudions les espaces analytiques rigides de dimension 1, réguliers, de genre fini sur un corps valué complet . Nous montrons qu’un tel espace admet une réduction préstable. Si est maximalement complet, se plonge dans une courbe algébrique (analytifiée). On donne aussi une caractérisation des espaces analytiques qui sont le complémentaire d’une partie compacte dans une courbe algébrique.
-adic analytic spaces.
-adic cycles
-adic Differential Operators on Automorphic Forms on Unitary Groups
The goal of this paper is to study certain -adic differential operators on automorphic forms on . These operators are a generalization to the higher-dimensional, vector-valued situation of the -adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the -adic case of the -differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain -adic...
-adic estimates for exponential sums and the theorem of Chevalley-Warning
-adic etale cohomology
-adic Fourier theory.
-adic heights for semi-stable abelian varieties
-adic Hodge theory in the semi-stable reduction case.
-adic interpolation of special values of Hecke L-functions