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arXiv · 1907.05838

Tamagawa number formula with coefficients over varieties in positive characteristic

Olivier Brinon·Fabien Trihan
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Abstract

We express the order of the pole and the leading coefficient of the L-function of a (large class of) -adic coefficients (any prime) over a quasi-projective variety over a finite field of characteristic p. This is a generalization of the result of Milne-Ramachandran with coefficients. The new key ingredient is the use of F-gauges and their equivalence in the derived category with Raynaud modules proved by Ekedahl.

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Olivier Brinon, Fabien Trihan. 2019-07-12. Tamagawa number formula with coefficients over varieties in positive characteristic. https://arxiv.org/abs/1907.05838

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