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Integral motives and special values of zeta functions


Authors: James S. Milne and Niranjan Ramachandran
Journal: J. Amer. Math. Soc. 17 (2004), 499-555
MSC (2000): Primary 11G09; Secondary 14F42, 14G10
DOI: https://doi.org/10.1090/S0894-0347-04-00458-8
Published electronically: April 26, 2004
MathSciNet review: 2053950
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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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Additional Information

James S. Milne
Affiliation: 2679 Bedford Road, Ann Arbor, Michigan 48104
Email: math@jmilne.org

Niranjan Ramachandran
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: atma@math.umd.edu

DOI: https://doi.org/10.1090/S0894-0347-04-00458-8
Received by editor(s): June 11, 2002
Published electronically: April 26, 2004
Additional Notes: The first author received support from the National Science Foundation and the second author from MPIM (Bonn) and a GRB Summer Grant (UMD)
Article copyright: © Copyright 2004 American Mathematical Society

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