**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

**Notes on Fermionic Fock Space for Number Theorists**

by

**Greg W. Anderson**-

**The University of Arizona**

This is a compilation of exercises, worked examples and key references that the author compiled in order to help readers learn their way around fermionic Fock space. The text is suitable for use by graduate students with an interest in number theory.

(

**12217**views)

**Algorithms for Modular Elliptic Curves**

by

**J. E. Cremona**-

**Cambridge University Press**

The author describes the construction of modular elliptic curves giving an algorithm for their computation. Then algorithms for the arithmetic of elliptic curves are presented. Finally, the results of the implementations of the algorithms are given.

(

**17680**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.

(

**12786**views)

**Pluckings from the tree of Smarandache: Sequences and functions**

by

**Charles Ashbacher**-

**American Research Press**

The third book in a series exploring the set of problems called Smarandache Notions. This work delves more deeply into the mathematics of the problems, the level of difficulty here will be somewhat higher than that of the previous books.

(

**17713**views)