Number Theory Seminar: Ashvin Swaminathan (Harvard University)

Title: Toward secondary terms for 2-Selmer groups in special families of elliptic curves

Abstract: A well-known result of Bhargava and Shankar states that when elliptic curves over Q are ordered by naive height, the average size of their 2-Selmer groups is equal to 3. But this result is at odds with computed tables of Selmer groups of elliptic curves, which indicate an average of slightly less than 3. Recent work of Shankar and Taniguchi suggests that the asymptotic count of 2-Selmer elements possesses a negative second-order term, which would explain the discrepancy. In this talk, we will discuss progress toward obtaining second-order asymptotics for 2-Selmer groups in special families of elliptic curves, such as the family of Mordell curves.

Spiegelgasse 5, Seminarraum 05.002

Veranstaltung übernehmen als iCal