## EVENT DETAILS AND ABSTRACT

**Number Theory**
**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.

**Date:** Monday, May 03, 2010

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Florian Herzig

**Contact email:** herzig@math

**Contact Phone:** 847-467-1898

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