Hurwitz trees and deformations of Artin-Schreier covers

Abstract: In this talk, we introduce the notion of Hurwitz tree for an Artin-Schreier deformation (deformation of $\mathbb{Z}/p$-covers in characteristic $p > 0$). It is a combinatorial-differential object that is endowed with essential degeneration data, measured by Kato's refined Swan conductors, of the deformation. We then show how the existence of a deformation between two covers with different branching data (e.g., different number of branch points) equates to the presence of a Hurwitz tree with behaviors determined by the branching data. One application of this result is to prove that the moduli space of Artin-Schreier covers of fixed genus $g$ is connected when $g$ is sufficiently large. If time permits, we will discuss a generalization of the Hurwitz tree technique to all cyclic covers and beyond.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

( paper )

Comments: Zoom ID: 625 5863 1654

Password: 809410

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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