Integral motives and special values of zeta functions

Milne, James; Ramachandran, Niranjan

doi:10.1090/S0894-0347-04-00458-8

Integral motives and special values of zeta functions
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by James S. Milne and Niranjan Ramachandran

J. Amer. Math. Soc. 17 (2004), 499-555

DOI: https://doi.org/10.1090/S0894-0347-04-00458-8

Published electronically: April 26, 2004

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Abstract:

For each field $k$, we define a category of rationally decomposed mixed motives with $\mathbb {Z}$-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 $\operatorname {Ext}$ groups.

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