Speaker: Zichao Lin (University of Massachusetts Amherst)

Title: On Iwasawa mu-invariants for Selmer groups over Z_2-extensions

Time: 14:00-15:00 July 23, 2026 (Thursday)

Place: MCM410

Abstract: Let E be an elliptic curve over Q with good ordinary reduction at p, E[p] the p-torsion points of E and Q_infty/Q the cyclotomic Z_p-extension. Further assume E[p] is reducible as a G_Q-representation over F_p. In 1999, Greenberg offered sufficient conditions for the Pontryagin dual of the Selmer group over Q_infty to have mu-invariant 0 and obtained a lower bound when the mu-invariant is positive. In this talk, we will focus on the p=2 case and provide an upper bound for the mu-invariants. Combining with Greenberg’s result, we are able to classify all the elliptic curves with mu-invariant 0 or 1 under the additional assumptions that E[4] is reducible. This is joint work with Mulun Yin.