textbooks are available on the E-book Directory. Algebraic Groups and Discontinuous Subgroups Algebraic Groups and Class Fields,Jean-Pierre Author: Kevin de Asis. This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in The translation is faithful to the original globally but, taking advantage of my being the translator of my own book, I felt completely free to reform or deform the original locally everywhere. Abstract: This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. This course is an introduction to algebraic number theory. We will follow Samuel's book Algebraic Theory of Numbers to start with, and later will switch to Milne's notes on Class Field theory, and lecture notes for other topics. There will be assigned readings for every class.

Jean-Pierre Serre, (born Septem , Bages, France), French mathematician who was awarded the Fields Medal in for his work in algebraic he was awarded the first Abel Prize by the Norwegian Academy of Science and Letters.. Serre attended the École Normale Supérieure (–48) and the Sorbonne (Ph.D.; ), both now part of the Universities of Paris. Algebraic number theory involves using techniques from (mostly commutative) algebra and nite group theory to gain a deeper understanding of the arithmetic of number elds and related objects (e.g., functions elds, elliptic curves, etc.). Algebraic and Arithmetic Geometry. Representations of Algebraic Groups Jantzen Foundations of Algebraic Geometry Vakil Algebraic Curves and Riemann Surfaces Miranda An Invitation to Arithmetic Geometry Lorenzini ; The Arithmetic of Elliptic Curves Silverman in progress complete. In I wrote out a brief outline, following Quillen's paper Higher algebraic K-theory I. It was overwhelming. I talked to Hy Bass, the author of the classic book Algebraic K-theory, about what would be involved in writing such a book. It was scary, because (in ) I didn't know even how to write a book.

The book is still remarkably up-to-date. It covers nearly all areas of the subject, although its approach is slanted somewhat toward class field theory. Some more recent texts with a similar approach and coverage include Lang’s Algebraic Number . Milne, Algebraic Number Theory. Milne’s course notes (in several sub-jects) are always good. Lang, Algebraic Number Theory. Murty, Esmonde, Problems in Algebraic Number Theory. This book was designed for self study. Lots of exercises with full solutions. Janusz, Algebraic Number Fields 8File Size: KB.