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SUMMARY:Huy Dang (University of Virginia)
DTSTART:20200520T050000Z
DTEND:20200520T060000Z
DTSTAMP:20260423T024738Z
UID:POINTS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINTS/5/">H
 urwitz trees and deformations of Artin-Schreier covers</a>\nby Huy Dang (U
 niversity of Virginia) as part of POINTS - Peking Online International Num
 ber Theory Seminar\n\n\nAbstract\nIn this talk\, we introduce the notion o
 f Hurwitz tree for an Artin-Schreier deformation (deformation of $\\mathbb
 {Z}/p$-covers in characteristic $p > 0$). It is a combinatorial-differenti
 al object that is endowed with essential degeneration data\, measured by K
 ato's refined Swan conductors\, of the deformation. We then show how the e
 xistence of a deformation between two covers with different branching data
  (e.g.\, different number of branch points) equates to the presence of a H
 urwitz tree with behaviors determined by the branching data. One applicati
 on of this result is to prove that the moduli space of Artin-Schreier cove
 rs 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.\n\nZoom ID: 625 5863 1654\n\nPassword: 80
 9410\n
LOCATION:https://researchseminars.org/talk/POINTS/5/
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