Étale cohomology, cofinite generation, and p-adic L-functions

Eisenstein Cohomology and p - adic L - Functions

§0. Introduction. In this paper, we define the module D̃(V ) of distributions with rational poles on a finite dimensional rational vector space a V . This is an infinite dimensional vector space over Q endowed with a natural action of the reductive group GV := Aut(V ). Indeed, this action extends to a natural action of the adelic group GV (AQ). For each prime p, we define we define the notion of...

Computing Zeta Functions via p-Adic Cohomology

We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

SUPERSINGULAR PRIMES AND p-ADIC L-FUNCTIONS

We discuss the problem of finding a p-adic L-function attached to an elliptic curve with complex multiplication over an imaginary quadratic field K, for the case of a prime where the curve has supersingular reduction. While the case of primes of ordinary reduction has been extensively studied and is essentially understood, yielding many deep and interesting results, basic questions remain unans...

p-adic Cohomology

The purpose of this paper is to survey some recent results in the theory of “p-adic cohomology”, by which we will mean several different (but related) things: the de Rham or p-adic étale cohomology of varieties over p-adic fields, or the rigid cohomology of varieties over fields of characteristic p > 0. Our goal is to update Illusie’s beautiful 1994 survey [I] by reporting on some of the many i...