Representations in Arithmetic Lectures: Antonio Lei

Let E/Q be an elliptic curve. In Iwasawa Theory, we study the behaviours of E over a tower of number fields. For example, it is known that the Mordell Weil ranks of E over all p-power cyclotomic extensions of Q are bounded when p does not divide the conductor of E. Surprisingly, the techniques required to show this are very different depending on the number of points on the finite curve when we consider E reduced modulo p. The easier case is when E has "ordinary" reduction at p and the more difficult case is when E has "supersingular" reduction at p. I will review the Iwasawa-theoretic tools used to study the behaviours of E over cyclotomic fields in these two cases. I will also discuss some recent developments on the Iwasawa theory of elliptic curves over quadratic extensions of Q.

This series of lectures will be delivered March 5, 7, 9 : 11 a.m- 12:30pm. More details are available below.