Integral Motives and Special Values of Zeta Functions

James S. Milne, Niranjan Ramachandran

Published 2002-04-05, updated 2002-05-24Version 2

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near integers to certain Ext groups. This is the submitted version, with minor corrections and additions from the first version.