## Annals of K-Theory

### On a localization formula of epsilon factors via microlocal geometry

#### Abstract

Given a lisse $l$-adic sheaf $G$ on a smooth proper variety $X$ and a lisse sheaf $ℱ$ on an open dense $U$ in $X$, Kato and Saito conjectured a localization formula for the global $l$-adic epsilon factor $ε l ( X , ℱ ⊗ G )$ in terms of the global epsilon factor of $ℱ$ and a certain intersection number associated to $det ( G )$ and the Swan class of $ℱ$. 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

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

Dates
Revised: 16 May 2017
Accepted: 23 July 2017
First available in Project Euclid: 24 July 2018

https://projecteuclid.org/euclid.akt/1532397765

Digital Object Identifier
doi:10.2140/akt.2018.3.461

Mathematical Reviews number (MathSciNet)
MR3830199

Zentralblatt MATH identifier
06911674

Keywords
K-theory epsilon factors

#### Citation

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. https://projecteuclid.org/euclid.akt/1532397765

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