14 citations · 22 across the 4 of their papers we have counts for
6 papers · 1 filter
Park City lectures on elliptic curves over function fields
Douglas Ulmer
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three…
Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
Douglas Ulmer
Our goal in this note is to give a number of examples of abelian varieties over function fields k(t) which have bounded ranks in towers of extensions such as k(t^{1/d}) for varying…
L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
Douglas Ulmer
The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many…
Elliptic curves and analogies between number fields and function fields
Douglas Ulmer
The well-known analogies between number fields and function fields have led to the transposition of many problems from one domain to the other. In this paper, we will discuss traff…
Geometric non-vanishing
Douglas Ulmer
We consider -functions attached to representations of the Galois group of the function field of a curve over a finite field. Under mild tameness hypotheses, we prove non-vanishi…
Elliptic curves with large rank over function fields
Douglas Ulmer
We produce explicit elliptic curves over \Bbb F_p(t) whose Mordell-Weil groups have arbitrarily large rank. Our method is to prove the conjecture of Birch and Swinnerton-Dyer for t…