Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to...
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shi...
This is the first of two volumes constituting The Legacy of Bernhard Riemann After One Hundred and Fifty Years. Bernhard Riemann (1826-1866) possessed an original and broad vision of mathematics together with powerful skill. His work continues to influence almost all major branches of mathematics. The twenty-three papers in the two-volume set examine Riemann, his work, and his significance in the context of modern mathematical developments. Contributing authors (to the two-volume set): Michael F. Atiyah, M. V. Berry, Ching-Li Chai, Brian Conrey, Jean-Pierre Demailly, F. T. Farrell,...
This is the first of two volumes constituting The Legacy of Bernhard Riemann After One Hundred and Fifty Years. Bernhard Riemann (1826-1866) posses...
This is the second of two volumes constituting The Legacy of Bernhard Riemann After One Hundred and Fifty Years. Bernhard Riemann (1826-1866) possessed an original and broad vision of mathematics together with powerful skill. His work continues to influence almost all major branches of mathematics. The twenty-three papers in the two-volume set examine Riemann, his work, and his significance in the context of modern mathematical developments. Contributing authors (to the two-volume set): Michael F. Atiyah, M. V. Berry, Ching-Li Chai, Brian Conrey, Jean-Pierre Demailly, F. T. Farrell,...
This is the second of two volumes constituting The Legacy of Bernhard Riemann After One Hundred and Fifty Years. Bernhard Riemann (1826-1866) posse...