The p-adic derived Hecke algebra and Stark units
Dr. Robin Zhang
2025-06-26 10:30-11:30
MCM610
Speaker: Dr. Robin Zhang (MIT)
Time: 10:30-11:30 June 26, 2025 (Thursday)
Venue: MCM610
Title: The p-adic derived Hecke algebra and Stark units
Abstract: The Harris–Venkatesh plus Stark conjecture says that the action of the derived Hecke algebra on weight-1 cusp forms describes Stark units modulo p for all but finitely many primes p. These derived Hecke operators H^0 → H^1 on the cohomology of modular curves are defined by Shimura classes arising from the cover of X_1(p) over X_0(p). I will report on in-progress work to describe p-adic Shimura classes, define derived Hecke operators on completed cohomology, and formulate a similar conjecture for p-adic regulators of Stark units.
