Cari tutti,
il prossimo seminario di geometria algebrica e aritmetica di Pisa si terrà mercoledì 2 marzo in Aula Magna del Dipartimento.
Programma:
14:30--15:30 Giulio Bresciani (SNS Pisa): Two results about Grothendieck's Section Conjecture
Grothendieck's Section Conjecture states that, if X is an hyperbolic curve over a field k finitely generated over Q, every section of the map π_1(X)→Gal(k) is associated with a rational point of the completion of X. After summarizing the main known facts concerning the conjecture, we will present two new results. First, we generalize to number fields a theorem which was proved over Q by Stix: we prove that if k is a number field and the Weil restriction of X to Q admits a rational map to a non-trivial Brauer-Severi variety, then X satisfies the conjecture. Secondly, if k is finitely generated over Q, we prove that the conjecture holds for sections which satisfy a strong birationality assumption. In particular, this implies that the section conjecture is equivalent to Esnault and Hai's cuspidalization conjecture, which states that every Galois section of every hyperbolic curve X lifts to every open subset of X.
NUOVO homepage del seminario: https://indico.cs.dm.unipi.it/category/4/
Migliori saluti, Tamás Szamuely