NW NUMBER THEORY SEMINAR, February 23rd, 2002

Place: Bond Hall 217, University of Western Washington, Bellingham, WA

First talk: 11-12

Matt Baker from Harvard University

Canonical heights over abelian varieties

Abstract: Let A be an abelian variety defined over a number field K, and let Kab denote the maximal abelian extension of K. We conjecture that there exists a constant C > 0 (depending on A and K) such that if P is a non-torsion point in A(Kab), then the canonical height of P is at least C. We will sketch a proof of the conjecture when A is an elliptic curve satisfying some additional hypotheses. We will also discuss some possible generalizations of the main conjecture.


Second talk: 2:00 - 2:45 PM

Imin Chen of Simon Fraser University

Elliptic curves with non-split mod 11 representations

Abstract: This talk will discuss a method to explicitly determine the j-invariants of elliptic curves corresponding to rational points on certain modular curves of level 11.


Third Talk: 3 - 3:45 PM

Adrian Iovita of the University of Washington

Families of exponential maps attached to p-adic families of modular forms

Abstract: A p-adic analytic family of modular forms produces on the one hand a family of Galois representations and on the other hand a two-variable p-adic L-function. The talk will show how these objects are directly related.