Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Slope Uniformity of Artin-Shreier-Witt Covers Over the Projective Line

Shichen Tang
Monday, October 28, 2019
5:00 pm - 5:50 pm
RH 440R

Talk Abstract:

Zeta function of a curve over a finite field carries the information of point count of the curve. A classical question in number theory is understanding the roots of the zeta function. Weil completely understood the archimedean absolute value of such roots, and the $\ell$-adic absolute values is known to be trivial. But the $p$-adic absolute value remains mysterious. Study of such absolute value can be reduced to study of the slopes of certain $L$-functions. In this talk I will present some known results related to patterns of $L$-functions of curves in Artin-Shreier-Witt towers, which is a tower of branched covers with Galois group $\mathbb{Z}_{p^\ell}$. Then I will discuss the general idea for the proof.

About the Speaker:

Shichen is a 4th year PhD student interested in number theory. In his spare time, he enjoys watching anime.

Refreshments:

Pizza will be served after the talk.