Product formula for p-adic epsilon factors

Tomoyuki Abe (1) , Adriano Marmora (2)

1 IPMU - Institute for the Physics and Mathematics of the Universe
2 IRMA - Institut de Recherche Mathématique Avancée

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 étale 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.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Tomoyuki Abe, Adriano Marmora. Product formula for p-adic epsilon factors. Journal of the Institute of Mathematics of Jussieu, 2015, 14 (2), ⟨10.1017/S1474748014000024⟩. ⟨hal-00585054⟩