*AVVISO SEMINARIO DI MATEMATICA*
Giovedì 10 marzo 2022
Aula Fermi
ore 16:00
Scuola Normale Superiore
Pisa
Dr. Guido Lido (Roma 2)
terrà un seminario dal titolo:
"Computations in the Poincaré torsor and the quadratic Chabauty method"
*Abstract:* (Joint work with Bas Edixhoven.) Falting's theorem states that a curve C of genus g>1 defined over the rationals has a finite number of rational points. In practice anyway there is no general procedure to provably compute the set C(Q). When the rank of the Mordell-Weil group J(Q) (with J the Jacobian of C) is smaller than g we can use Chabauty method, i.e. we can embed C in J and, after choosing a prime p, we can view C(Q) as a subset of the intersection of C(Q_p) and the closure of J(Q) inside the p-adic manifold J(Q_p); this intersection is always finite and computable up to finite precision. Minhyong Kim has generalized this method by inspecting (possibly non-abelian) quotients of the fundamental group of C. His ideas have been made effective in some new cases by Balakrishnan, Dogra, Muller, Tuitman and Vonk: their "quadratic Chabauty method" works when the rank of the Mordell-Weil group is strictly less than g + s -1 (with s the rank of the Neron-Severi group of J). In the seminar we will give a reinterpretation of the quadratic Chabauty method, only using the Poincaré torsor of J and a little of formal geometry, and we will show how to make it effective.
Il seminario si terrà in presenza. Chi fosse interessato a partecipare in presenza deve scrivere a andrea.ferraguti@sns.it entro le 10:00 di Giovedì 10 marzo 2022. Classe di Scienze
Valeria Giuliani Scuola Normale Superiore Servizio Attività Didattiche tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it
Valeria Giuliani Scuola Normale Superiore Servizio Attività Didattiche tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it
Il giorno lun 28 feb 2022 alle ore 10:23 Valeria Giuliani < valeria.giuliani@sns.it> ha scritto:
*AVVISO SEMINARIO DI MATEMATICA*
Giovedì 10 marzo 2022
Aula Fermi
ore 16:00Scuola Normale Superiore
Pisa
Dr. Guido Lido (Roma 2)
terrà un seminario dal titolo:
"Computations in the Poincaré torsor and the quadratic Chabauty method"
*Abstract:* (Joint work with Bas Edixhoven.) Falting's theorem states that a curve C of genus g>1 defined over the rationals has a finite number of rational points. In practice anyway there is no general procedure to provably compute the set C(Q). When the rank of the Mordell-Weil group J(Q) (with J the Jacobian of C) is smaller than g we can use Chabauty method, i.e. we can embed C in J and, after choosing a prime p, we can view C(Q) as a subset of the intersection of C(Q_p) and the closure of J(Q) inside the p-adic manifold J(Q_p); this intersection is always finite and computable up to finite precision. Minhyong Kim has generalized this method by inspecting (possibly non-abelian) quotients of the fundamental group of C. His ideas have been made effective in some new cases by Balakrishnan, Dogra, Muller, Tuitman and Vonk: their "quadratic Chabauty method" works when the rank of the Mordell-Weil group is strictly less than g + s -1 (with s the rank of the Neron-Severi group of J). In the seminar we will give a reinterpretation of the quadratic Chabauty method, only using the Poincaré torsor of J and a little of formal geometry, and we will show how to make it effective.
Il seminario si terrà in presenza. Chi fosse interessato a partecipare in presenza deve scrivere a andrea.ferraguti@sns.it entro le 10:00 di Giovedì 10 marzo 2022. Classe di Scienze
Valeria Giuliani Scuola Normale Superiore Servizio Attività Didattiche tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it
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Valeria Giuliani