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AROUND THE NEARBY CYCLE FUNCTOR FOR ARITHMETIC $\mathscr{D}$-MODULES

Part of: (Co)homology theory

Published online by Cambridge University Press:  28 August 2019

TOMOYUKI ABE
TOMOYUKI ABE*
Affiliation:
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8583, Japan email tomoyuki.abe@ipmu.jp
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Abstract

We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathscr{D}$-module theory following Beilinson’s philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathscr{D}$-modules whose category is equivalent to the category of overconvergent isocrystals.

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F30: $p$-adic cohomology, crystalline cohomology
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 1 - 28
Copyright
© 2019 Foundation Nagoya Mathematical Journal  

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