**Elliptic Curves over Function Fields**

by Douglas Ulmer

**Publisher**: arXiv 2011**Number of pages**: 72

**Description**:

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 lectures, we explain the main classical results (mainly due to Tate) on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces.

Download or read it online for free here:

**Download link**

(670KB, PDF)

## Similar books

**Collections of Problems on Smarandache Notions**

by

**Charles Ashbacher**-

**Erhus University Press**

This text deals with some advanced consequences of the Smarandache function. The reading of this book is a form of mindjoining, where the author tries to create the opportunity for a shared experience of an adventure.

(

**12844**views)

**Arithmetic Duality Theorems**

by

**J.S. Milne**-

**BookSurge Publishing**

This book, intended for research mathematicians, proves the duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry, for example, in the proof of Fermat's Last Theorem.

(

**11384**views)

**Introduction to Shimura Varieties**

by

**J.S. Milne**

This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms. Because of their brevity, many proofs have been omitted or only sketched.

(

**5108**views)

**Harmonic Analysis, the Trace Formula, and Shimura Varieties**

by

**J. Arthur, D. Ellwood, R. Kottwitz**-

**American Mathematical Society**

The goal of this volume is to provide an entry point into the challenging field of the modern theory of automorphic forms. It is directed on the one hand at graduate students and professional mathematicians who would like to work in the area.

(

**7664**views)