Time：15:00-16:00, Thursday, September 25 2025
Venue: E4-233
Speaker：Dingxin Zhang, Shanghai Institute for Mathematics and Interdisciplinary Sciences & Fudan University
Title：Cohomological divisibility of exponential sum
Abstract：40 odd years ago, Adolphson and Sperber showed that the q-divisibility of complete exponential sums over F_q can be bounded by a specific combinatorial quantity using Dwork theory. While their result is p-adic in nature, the "independence of ℓ" conjecture suggests that the Frobenius eigenvalues of the ℓ-adic Artin-Schreier cohomology associated with these exponential sums should exhibit identical divisibility properties for every prime ℓ not dividing q. In this talk, I will present recent work in progress toward proving this divisibility for Frobenius eigenvalues.
