Wei Zhang - Cycles on products of elliptic curves and a conjecture of Beilinson/Bloch-Kato

March 23, 2022 - This is the second in a series of three Minerva Lectures.
In the second talk, we will move to certain high dimensional varieties (such as the product of several elliptic curves) over number fields, where, instead of rational points, we want to search for (or to show finiteness of) algebraic cycles (i.e., parameter solutions) modulo suitable equivalence relations (rational equivalence, Abel-Jacobi or its p-adic variants). In particular, we’ll report some recent results on a conjecture of Beilinson/Bloch-Kato and the role of the Gan-Gross-Prasad (or the arithmetic diagonal) cycle in the proof.