Number Theory Seminar

Seminar information archive ~04/21Next seminarFuture seminars 04/22~

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


13:00-16:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Lasse Grimmelt (University of Göttingen/Waseda University) 13:00-14:00
Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)
Haoyu Hu (University of Tokyo) 14:15-15:15
Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)
[ Abstract ]
I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.
Yasuhiro Wakabayashi (University of Tokyo) 15:30-16:30
Explicit computation of the number of dormant opers and duality (Japanese)