Variations on a Theorem of Tate - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variations on a Theorem of Tate write by Stefan Patrikis. This book was released on 2019-04-10. Variations on a Theorem of Tate available in PDF, EPUB and Kindle. Let F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.
Arithmetic Duality Theorems
Arithmetic Duality Theorems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Arithmetic Duality Theorems write by J. S. Milne. This book was released on 1986. Arithmetic Duality Theorems available in PDF, EPUB and Kindle. Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Variations on a Theorem of Tate
Variations on a Theorem of Tate - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variations on a Theorem of Tate write by Stefan Patrikis. This book was released on 2019. Variations on a Theorem of Tate available in PDF, EPUB and Kindle.
Rational Points on Elliptic Curves
Rational Points on Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rational Points on Elliptic Curves write by Joseph H. Silverman. This book was released on 2013-04-17. Rational Points on Elliptic Curves available in PDF, EPUB and Kindle. The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Mumford-Tate Groups and Domains
Mumford-Tate Groups and Domains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mumford-Tate Groups and Domains write by Mark Green. This book was released on 2012-04-22. Mumford-Tate Groups and Domains available in PDF, EPUB and Kindle. Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
