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On the zeroes and poles of L-functions over varieties in positive characteristic

  • Fabien Trihan EMAIL logo and Olivier Brinon ORCID logo
Published/Copyright: June 25, 2022

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. We use the technique of [13] with coefficients with, as new ingredient, the use of F-gauges and their equivalence, in the derived category, with Raynaud modules proved by Ekedahl.

Acknowledgements

We would like to express our gratitude to Kazuya Kato, Atsushi Shiho and Takashi Suzuki for very enlightning discussions about the appropriate category of coefficients for our result. We also would like to thank the referee for his careful reading and help to improve the presentation of the paper.

References

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Received: 2020-07-14
Revised: 2021-09-16
Published Online: 2022-06-25
Published in Print: 2022-08-01

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