Arithmetic Algebraic Geometry (IAS/Park City Mathematic) (Ias/Park City Mathematic)

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. 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 The 1999 Graduate Summer School of the Institute for Advanced Study/Park City Mathematics Institute was held in Park City, Utah from June 20 to July 10, 1999. Brian Conrad, Karl Rubin, Editors. Includes Bibliographical References (p. 565-569).