Number Theory Seminar

Seminar information archive ~12/10Next seminarFuture seminars 12/11~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly


17:00-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Daichi Takeuchi (University of Tokyo)
Characteristic epsilon cycles of l-adic sheaves on varieties (ENGLISH)
[ Abstract ]
For l-adic sheaves on varieties over finite fields, the constant terms of the functional equations of the L-functions, called global epsilon factors, are important arithmetic invariants. When the varieties are curves, Deligne and Laumon show that they admit product formulae in terms of local epsilon factors.
In this talk, I will explain that, attaching some coefficients to irreducible components of singular supports, we can define refinements of characteristic cycles. We will see that, after taking modulo roots of unity, they give product formulae of global epsilon factors for higher dimensional varieties.
I will also explain that these results can be generalized to arbitrary perfect fields of any characteristic.