欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
科学研究
RESEARCH
Seminars on Dwork Theory-3:$p$-adic estimates of exponential sums on curves
时间  Datetime
2021-01-05 09:00 — 10:00
地点  Venue
Zoom APP()
报告人  Speaker
Joe Kramer-Miller
单位  Affiliation
University of California, Irvine
邀请人  Host
Jiyou Li
备注  remarks
Zoom No.: 922 327 63848 Passcode: 121212
报告摘要  Abstract

Let $X$ be a smooth proper curve over a finite field
$\mathbb{F}_q$ of characteristic $p\geq 3$ and let $V \subset X$ be an
affine curve. For a regular function $\overline{f}$ on $V$, we may form
the $L$-function $L(\overline{f},V,s)$ associated to the exponential
sums of $\overline{f}$. We prove a lower estimate on the Newton polygon
of $L(\overline{f},V,s)$. This confirms a conjecture of Deligne that the
"irregular Hodge filtration forces bounds on $p$-adic valuations of
Frobenius eigenvalues. We will explain the main strategy underlying the
proof. This strategy was subsequently applied in joint work with James
Upton to study $\mathbb{Z}_p$-towers over ordinary curves.