Arithmetic algebraic geometry

Brian David Conrad, Karl Rubin0821821733, 9780821821732

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat’s Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

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Table of contents :
Contents.pdf……Page 1
Preface.pdf……Page 9
Introduction.pdf……Page 11
Elliptic Curves, Modular Forms, and Applications.pdf……Page 15
Open Questions in Arithmetic Algebraic Geometry.pdf……Page 92
Lectures on Serre’s Conjectures.pdf……Page 152
Deformations of Galois Representations.pdf……Page 244
Introduction to Iwasawa Theory for Elliptic Curves.pdf……Page 418
Galois Cohomology.pdf……Page 476
The Arithmetic of Modular Forms.pdf……Page 493
Arithmetic of Certain Calabi-Yau Varieties and Mirror Symmetry.pdf……Page 515