ON THE ETALE COHOMOLOGY OF TORSORS FOR ABELIAN SCHEMES

Abstract

We study the Leray spectral sequence for the integral l-adic cohomology of torsors for abelian schemes. For an abelian scheme over a smooth, geometrically irreducible curve over a finite field, we relate the question of whether a torsor is determined by its etale cohomology with the conjectured finiteness of the set of all such torsors.