Product formula for p-adic epsilon factors
Algebraic Geometry
2014-05-14 v3 Number Theory
Abstract
Let X be a smooth proper curve over a finite field of characteristic p. We prove a product formula for p-adic epsilon factors of arithmetic D-modules on X. In particular we deduce the analogous formula for overconvergent F-isocrystals, which was conjectured previously. The p-adic product formula is the equivalent in rigid cohomology of the Deligne-Laumon formula for epsilon factors in l-adic \'etale cohomology (for a prime l different from p). One of the main tools in the proof of this p-adic formula is a theorem of regular stationary phase for arithmetic D-modules that we prove by microlocal techniques.
Cite
@article{arxiv.1104.1563,
title = {Product formula for p-adic epsilon factors},
author = {Tomoyuki Abe and Adriano Marmora},
journal= {arXiv preprint arXiv:1104.1563},
year = {2014}
}
Comments
Revised version: some proofs and constructions detailed, notation improved, index of notation added ; 88 pages