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Product formula for p -adic epsilon factors
Published online by Cambridge University Press: 08 May 2014
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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- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 2 , April 2015 , pp. 275 - 377
- Copyright
- © Cambridge University Press 2014
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