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Product formula for p -adic epsilon factors

  • Tomoyuki Abe (a1) and Adriano Marmora (a2)

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 $\mathscr{D}$ -modules on $X$ . In particular we deduce the analogous formula for overconvergent $F$ -isocrystals, which was conjectured previously. The $p$ -adic product formula is a counterpart in rigid cohomology of the Deligne–Laumon formula for epsilon factors in $\ell$ -adic étale cohomology (for $\ell \neq p$ ). One of the main tools in the proof of this $p$ -adic formula is a theorem of regular stationary phase for arithmetic $\mathscr{D}$ -modules that we prove by microlocal techniques.

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Product formula for p -adic epsilon factors

  • Tomoyuki Abe (a1) and Adriano Marmora (a2)

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