Seminario di Geometria

Giovedì 17 Novembre alle ore 14:15, Guido Lido (Università degli Studi di Roma Tor Vergata) terrà il seminario di Geometria dal titolo "Computations in the Poincaré torsor and the quadratic Chabauty method".

Abstract: We know by Falting's theorem that a curve C of genus g>1 defined over the rationals has a finite number of rational points, but 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(Qp) 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. This is joint work with Bas Edixhoven.

Il seminario sarà presentato in presenza nell'aula M1. Per ulteriori informazioni si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.

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