Euler Characteristics and Special Values of Zeta-Functions

This article gives evidence for the philosophy that all special values of arithmetic zeta and L-functions are given by Emler characteristics. We treat here the case of L-functions of 1-motives, where we indicate what the answer ought to be, and sketch an argument showing that this answer is correct up to a rational number modulo the conjecture of Birch and Swinnerton-Dyer.