Vol. 3, No. 3, 2018

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ISSN: 2379-1691 (e-only)
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On a localization formula of epsilon factors via microlocal geometry

Tomoyuki Abe and Deepam Patel

Vol. 3 (2018), No. 3, 461–490
Abstract

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 εl(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 DX-modules on smooth projective varieties over a field of characteristic zero.

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