Time: 9:00 - 11:00, November 4, 2020

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In this talk, we introduce the Hurwitz tree's notion for abelian coverings of a rigid disc. It is a combinatorial-differential object endowed with the cover's essential degeneration data measured by (Kazuya) Kato's refined Swan conductor. We then discuss how to use these trees to study the moduli space that parametrizes Galois covers and their invariants (e.g., p-rank, a-number, Newton polygon). For instance, the technique was used to show that the moduli space of Artin-Schreier covers (Z/p-covers of the projective line in characteristic p) of fixed genus g is connected when g is large.