Quadratic Chabauty and beyond

Seminar
Speaker
Dr. David Corwin (Ben-Gurion University of the Negev)
Date
15/12/2021 - 11:30 - 10:30Add to Calendar 2021-12-15 10:30:00 2021-12-15 11:30:00 Quadratic Chabauty and beyond I will describe my work (some joint with I. Dan-Cohen) to extend the computational boundary of Kim's non-abelian Chabauty's method beyond the highly-studied Quadratic Chabauty. Faltings' Theorem says that the number of rational points on curves of higher genus is finite, and non-abelian Chabauty provides a blueprint both for proving this finiteness and for computing the sets of rational points. We first review classical Chabauty-Coleman, which does the same but works only for certain curves. Then we describe Kim's non-abelian generalization, which replaces abelian varieties in Chabauty-Coleman by Selmer groups (a kind of Galois cohomology) and eventually "non-abelian" Selmer varieties. Finally, we describe recent work in attempting to compute these sets using the theory of Tannakian categories. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062 Third floor seminar room, Mathematics building, and on Zoom. See link below. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room, Mathematics building, and on Zoom. See link below.
Abstract

I will describe my work (some joint with I. Dan-Cohen) to extend the computational boundary of Kim's non-abelian Chabauty's method beyond the highly-studied Quadratic Chabauty. Faltings' Theorem says that the number of rational points on curves of higher genus is finite, and non-abelian Chabauty provides a blueprint both for proving this finiteness and for computing the sets of rational points. We first review classical Chabauty-Coleman, which does the same but works only for certain curves. Then we describe Kim's non-abelian generalization, which replaces abelian varieties in Chabauty-Coleman by Selmer groups (a kind of Galois cohomology) and eventually "non-abelian" Selmer varieties. Finally, we describe recent work in attempting to compute these sets using the theory of Tannakian categories.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 12/12/2021