Πέμπτη, 7 Νοεμβρίου 2019, 10:15-11:00, Αίθουσα Μ2
Ομιλητής: Σωτήρης Καρανικολόπουλος, ΕΚΠΑ
Τίτλος: Automorphisms of Curves and Weierstrass semigroups
Περίληψη: Let X be a projective nonsingular algebraic curve defined over an algebraically closed field of positive characteristic p. I consider Harbater-Katz-Gabber covers: these are p-group Galois covers from X to P^1 with only one fully ramified point. This simple construction provide us with examples of curves with “huge” number of automorphisms; they are important because of their applications over finite fields and the Harbater-Katz-Gabber compactification theorem for Galois actions on complete local rings. The sequences of the jumps of the higher ramification filtrations of their Galois group are related to the Weierstrass semigroup of the global cover at the ramified point. I will compute these jumps in terms of the pole numbers and, if time permits, give some applications for curves with zero p-rank: maximal curves and curves that admit a “big action”.