Focusing on qualitative algebraic geometry, this book serves as an introduction to the Weil-Zariski framework, expanding on lectures from a series of courses initiated by Zariski. It provides a comprehensive overview of Weil's "Foundations" and contextualizes the development of modern algebraic geometry prior to the introduction of sheaves. This reprint preserves the original text, offering readers an authentic experience of the foundational concepts in the field.
Based on the work in algebraic geometry by Norwegian mathematician Niels Henrik Abel (1802–29), this monograph was originally published in 1959 and reprinted later in author Serge Lang's career without revision. The treatment remains a basic advanced text in its field, suitable for advanced undergraduates and graduate students in mathematics. Prerequisites include some background in elementary qualitative algebraic geometry and the elementary theory of algebraic groups. The book focuses exclusively on Abelian varieties rather than the broader field of algebraic groups; therefore, the first chapter presents all the general results on algebraic groups relevant to this treatment. Each chapter begins with a brief introduction and concludes with a historical and bibliographical note. Topics include general theorems on Abelian varieties, the theorem of the square, divisor classes on an Abelian variety, functorial formulas, the Picard variety of an arbitrary variety, the I-adic representations, and algebraic systems of Abelian varieties. The text concludes with a helpful Appendix covering the composition of correspondences.
This four-volume set showcases the significant research contributions of renowned mathematician Serge Lang across various fields. It compiles key papers that reflect his influence and advancements in mathematics, offering valuable insights into his work and legacy.
The collection features key research papers by renowned mathematician Serge Lang, showcasing his significant contributions across various fields in mathematics. As part of a four-volume set, it serves as a valuable resource for understanding Lang's impact and the breadth of his work in the mathematical community.
The book highlights the life and accomplishments of Serge Lang, a prominent mathematician known for his significant contributions to the field. Born in Paris and later moving to California, Lang's academic journey includes graduating from Beverly Hills High School, California Institute of Technology, and earning a doctorate from Princeton University. His career includes teaching positions at prestigious institutions like the University of Chicago and Columbia University, culminating in his role as professor emeritus at Yale University at the time of his passing.
The collection features significant research papers by renowned mathematician Serge Lang, showcasing his extensive contributions across various fields in mathematics. As part of a four-volume set, it serves as a valuable resource for understanding Lang's influential work and its impact on the mathematical community.
The collected papers showcase the significant contributions of Serge Lang, a leading figure in mathematics recognized for his exceptional work. His accolades include the prestigious Cole Prize from the American Mathematical Society and the Prix Carrière from the French Academy of Sciences, highlighting his impact and expertise in the field. This collection reflects his profound influence on mathematical thought and research.
The book presents a comprehensive exploration of classical algebraic and analytic number theory, expanding on previous works to include class field theory. It emphasizes a global perspective while addressing local fields only briefly. The author integrates ideal and idelic approaches, offering two distinct proofs of the functional equation for the zeta function to showcase various techniques. The text references influential literature and highlights the enduring relevance of historical cases in advancing theoretical understanding.
Exploring the fascinating realm of number theory, this book delves into cyclotomic fields, highlighting their significance in classical number theory and K-theory. It provides comprehensive coverage of advanced topics such as p-adic L-functions and Iwasawa theory, making it a valuable resource for those interested in the intricate connections between these mathematical concepts.
Focusing on fundamental concepts in differential topology, geometry, and equations, this expanded edition introduces three new chapters dedicated to Riemannian and pseudo-Riemannian geometry. It also features updated sections on sprays and Stokes' theorem, enriching the content for readers interested in advanced mathematical theories and applications.
