Ruprecht-Karls-Universität Heidelberg
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„Plectic Jacobians“
Dr. Lennart Gehrmann, Universität Duisburg-Essen

Heegner points play an important role in our understanding of the arithmetic of modular elliptic curves. These points, that arise from CM points on Shimura curves, control the Mordell-Weil group of elliptic curves of rank 1. The work of Bertolini, Darmon and their schools has shown that p-adic methods can be successfully employed to generalize the definition of Heegner points to quadratic extensions that are not necessarily CM. Numerical evidence strongly supports the belief that these so-called Stark-Heegner points completely control the Mordell-Weil group of elliptic curves of rank 1. Inspired by Nekovar and Scholl's plectic conjectures, Michele Fornea and I recently proposed a plectic generalization of Stark--Heegner points: a cohomological construction of elements in the completed tensor product of local points of elliptic curves that should control Mordell-Weil groups of higher rank. In this talk, focusing on the quadratic CM case, I will present an alternative speculative framework that can be used to cast the definition of plectic Stark-Heegner points in geometric terms. More precisely, given a variety X that admits uniformization by a product of p-adic upper half planes I will construct: - a subgroup of the group of zero-cycles of X, called plectic zero cycles of X - a topolgoical group, called the plectic Jacobian of X - a plectic Abel-Jacobi map, i.e. a map from plectic zero cycles to the plectic Jacobian

Freitag, den 3. Dezember 2021 um 13:30 Uhr, in INF205, SR A Freitag, den 3. Dezember 2021 at 13:30, in INF205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. Peter Gräf