Product formula for p adic epsilon factors

ar X iv :1 10 4. 15 63 v2 [ ma th. AG ] 31 M ay 20 11 Product formula for p-adic epsilon factors Tomoyuki Abe, Adriano Marmora 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 ?-adic etale cohomology (for ? 6= 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. Contents 1 Stability theorem for characteristic cycles on curves 6 1.1 Review of microdifferential operators . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Setup and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Relations between microlocalizations at different levels . . . . .

• adic product


• local fourier


• regular holonomic


• adic epsilon


• equality between


• fourier transform


• noot-huyghe


• concerning ?-adic