报告人：曹炜 （闽南师范大学）

题目：Divisibility on point counting over finite Witt rings

摘要：Let F_q denote the finite field of q elements with characteristic p. Let Z_q denote the unramified extension of the p-adic integers Z_p with residue field F_q. In a joint work with Prof. Daqing Wan, we study the q-divisibility for the number of solutions of a polynomial system in n variables over the finite Witt ring Z_q/p^mZ_q, where the n variables of the polynomials are restricted to run through a combinatorial box lifting F_q^n. We prove a q-divisibility theorem for any box of low algebraic complexity, including the simplest Teichmuller box. This extends the classical Ax-Katz theorem over finite field F_q (the case m=1). Taking q=p to be a prime, our result extends and improves a recent combinatorial theorem of Grynkiewicz. Our different approach is based on the addition operation of Witt vectors and is conceptually much more transparent.

时间：2022-12-07

地点：腾讯会议ID：358 9878 8585