EVENT DETAILS AND ABSTRACT

Title: Mordell-Weil ranks in towers of modular Jacobians
Speaker: Guillermo Mantilla-Soler
Speaker Info: Wisconsin
Brief Description:
Special Note:
Abstract:

In this talk we describe a technique to bound the growth of Mordell-Weil ranks in towers of Jacobians of modular curves. In more detail, we will show our progress towards the following result. Let p > 2 be a prime, and let J_n be the Jacobian of the principal modular curve X(p^n). Let F be a number field with mu-invariant mu, and such that Q(J_1[p]) is contained in F. We show that there exists a constant C, depending on F and p, such that rank J_n(F) is at most (2[F:Q] + 4 mu) dim J_n + C p^{2n} for all n.