#### Vol. 3, No. 3, 2018

 Recent Issues Volume 3, Issue 3 Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 4 Volume 2, Issue 3 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 4 Volume 1, Issue 3 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal About the Journal Subscriptions Editorial Board Ethics Statement Submission Guidelines Submission Form Editorial Login Ethics Statement Author Index To Appear Contacts ISSN: 2379-1691 (e-only) ISSN: 2379-1683 (print)
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 $\mathsc{G}$ on a smooth proper variety $X$ and a lisse sheaf $\mathsc{ℱ}$ on an open dense $U$ in $X$, Kato and Saito conjectured a localization formula for the global $l$-adic epsilon factor ${\epsilon }_{l}\left(X,\mathsc{ℱ}\otimes \mathsc{G}\right)$ in terms of the global epsilon factor of $\mathsc{ℱ}$ and a certain intersection number associated to $det\left(\mathsc{G}\right)$ and the Swan class of $\mathsc{ℱ}$. In this article, we prove an analog of this conjecture for global de Rham epsilon factors in the classical setting of ${\mathsc{D}}_{X}$-modules on smooth projective varieties over a field of characteristic zero.

##### Keywords
K-theory, epsilon factors
##### Mathematical Subject Classification 2010
Primary: 14C35, 14F10, 19M05