Annals of K-Theory

On a localization formula of epsilon factors via microlocal geometry

Tomoyuki Abe and Deepam Patel

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Given a lisse l -adic sheaf G on a smooth proper variety X and a lisse sheaf on an open dense U in X , Kato and Saito conjectured a localization formula for the global l -adic epsilon factor ε l ( X , G ) in terms of the global epsilon factor of and a certain intersection number associated to det ( G ) and the Swan class of . In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of D X -modules on smooth projective varieties over a field of characteristic zero.

Article information

Ann. K-Theory, Volume 3, Number 3 (2018), 461-490.

Received: 3 February 2017
Revised: 16 May 2017
Accepted: 23 July 2017
First available in Project Euclid: 24 July 2018

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Zentralblatt MATH identifier

Primary: 14C35: Applications of methods of algebraic $K$-theory [See also 19Exx] 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 19M05: Miscellaneous applications of $K$-theory

K-theory epsilon factors


Abe, Tomoyuki; Patel, Deepam. On a localization formula of epsilon factors via microlocal geometry. Ann. K-Theory 3 (2018), no. 3, 461--490. doi:10.2140/akt.2018.3.461.

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