On a localization formula of epsilon factors via microlocal geometry

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 $ε_{l} (X, ℱ \otimes G)$ 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.

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Keywords

K-theory, epsilon factors

Mathematical Subject Classification 2010

Primary: 14C35, 14F10, 19M05

Milestones

Received: 3 February 2017

Revised: 16 May 2017

Accepted: 23 July 2017

Published: 16 July 2018

Authors

Tomoyuki Abe
Kavli Institute for the Physics and Mathematics of the Universe (WPI) University of Tokyo Chiba Japan

Deepam Patel
Department of Mathematics Purdue University West Lafayette, IN United States

Vol. 3, No. 3, 2018

Tomoyuki Abe and Deepam Patel

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors