Scusate, questa è l'ultima mail:
il prossimo seminario di geometria algebrica e aritmetica di Pisa si terrà mercoledì 16 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 ________________________________________ Da: Geometria_Pisa geometria_pisa-bounces@fields.dm.unipi.it per conto di Tamas Szamuely tamas.szamuely@unipi.it Inviato: giovedì 10 marzo 2022 16:02:24 A: geometria_pisa@fields.dm.unipi.it; dottorandi@dm.unipi.it; Gabriele Vezzosi; Umberto Zannier; luca.migliorini.math@gmail.com; Francesco Sala; michele.pernice@sns.it; guglielmo.nocera@sns.it; andrea.ferraguti@sns.it; Gregory James Pearlstein; Luca Morstabilini; Davide Lombardo; Giovanni Gaiffi; Andrea Maffei; giulio.bresciani@sns.it; giulio.grammatica@sns.it; jacobbb84@gmail.com; valerio.melani@unifi.it Oggetto: [Geometria_pisa] Seminario di geometria algebrica e aritmetica, 17/03/2022
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
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