Wild Ramification and Some Problems of "Independence of ℓ"

Abstract

has coefficients in Z (rather than in Qe ) and if, for each given i, the Z-polynomial Pi,e (T) is of the auxiliary choice of ? p. That a proper and smooth X/Fq is independent of f results instantly from Deligne's fundamental result [1]. In this paper we will combine Deligne's techniques with his trick [2] of systematically twisting by very wildly ramified characters to show that independence of f also holds for proper varieties which are suitable limits of proper smooth varieties, and for certain related open varieties. Here is a precise statement: