Let F be a number field, and let f be a normalized eigenform of weight 2 and level N for GL(2,F). It is conjectured that attached to f there is an abelian variety A_f. This abelian variety should have dimension equal to the degree of the field of Hecke eigenvalues, and should have good reduction outside N. In those instances where the Eichler-Shimura construction is not available (for example when F is not totally-real) little is known about how to find A_f. In joint work with Xavier Guitart, we present a p-adic conjectural construction (subject to several restrictions, in particular p should divide N) of A_f, and illustrate how in favourable situations it can be used to find equations for abelian surfaces A_f as jacobians of hyperelliptic curves.
Freitag, den 12. Mai 2017 um 13:30 Uhr, in INF205, SR A Freitag, den 12. Mai 2017 at 13:30, in INF205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Gebhard Böckle