Abelian Varieties: Natural Products to Make for You and Your Home

Book Details

• Author: Serge Lang

• Publisher: Dover

• Language: English

• Edition: Reprint

• ISBN: 9780486828053

• Pages: 272

• Cover: Paperback

• Dimensions: 8.9 x 6.0 x 0.6 inches

About The Book

Abelian Varieties by Serge Lang is a foundational text in algebraic geometry, focusing on the work of Norwegian mathematician Niels Henrik Abel (1802–29). Originally published in 1959 and reprinted later in Lang's career, this book remains a key reference for advanced students and researchers in the field.

This monograph is ideal for advanced undergraduates and graduate students who have a background in elementary algebraic geometry and the elementary theory of algebraic groups. It delves deeply into Abelian varieties, offering a comprehensive and rigorous study, while avoiding the broader scope of algebraic groups.

Key features of the book include:

• Focused Treatment on Abelian Varieties: Unlike other texts in algebraic geometry, this book is dedicated specifically to Abelian varieties, providing detailed results and theorems relevant to this subject.

• Comprehensive and Accessible: Each chapter begins with an introduction to the topic and concludes with a historical and bibliographical note, making the material approachable while providing context and references for further study.

• In-depth Coverage: Topics include general theorems on Abelian varieties, divisor classes, the Picard variety, functorial formulas, and the I-adic representations, all presented with clarity and precision.

• Mathematical Foundations: The book starts with essential results on algebraic groups and builds upon them to explore the structure and theory of Abelian varieties.

• Helpful Appendices: The book concludes with an Appendix that covers the composition of correspondences, providing additional insights into advanced concepts.

Abelian Varieties is a classic text that serves as both a comprehensive introduction and an advanced reference for anyone interested in algebraic geometry and the study of Abelian varieties. Its precise treatment and historical context make it a valuable resource for both students and mathematicians.