
The central topic of this research monograph is the relation between padic modular forms and padic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the padic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the...




Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.




In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics: " basic real and complex analysis, ab stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit...




There is now a large body of theory concerning algebraic varieties over finite fields, and many conjectures in this area are of great interest to researchers in number theory and algebraic geometry. This book deals with the arithmetic of diagonal hypersurfaces over finite fields, with special focus on the Tate conjecture and the LichtenbaumMilne formula for the central value of the Lfunction....




Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π? ... negative numbers? ... the metric system? ... quadratic equations? ... sine and cosine? ... logs? Including five new independent historical sketches, each complete with added questions and projects, this second edition answers these questions and many others in an informal, easygoing...


