Vol. 3, No. 3, 2018

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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

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.

K-theory, epsilon factors
Mathematical Subject Classification 2010
Primary: 14C35, 14F10, 19M05
Received: 3 February 2017
Revised: 16 May 2017
Accepted: 23 July 2017
Published: 16 July 2018
Tomoyuki Abe
Kavli Institute for the Physics and Mathematics of the Universe (WPI)
University of Tokyo
Deepam Patel
Department of Mathematics
Purdue University
West Lafayette, IN
United States