The Norm Residue Theorem in Motivic Cohomology - 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 The Norm Residue Theorem in Motivic Cohomology write by Christian Haesemeyer. This book was released on 2019-06-11. The Norm Residue Theorem in Motivic Cohomology available in PDF, EPUB and Kindle. This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations. Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
The Norm Residue Theorem in Motivic Cohomology
The Norm Residue Theorem in Motivic Cohomology - 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 The Norm Residue Theorem in Motivic Cohomology write by Christian Haesemeyer. This book was released on 2019-06-11. The Norm Residue Theorem in Motivic Cohomology available in PDF, EPUB and Kindle. This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They proceed to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations. Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
Lecture Notes on Motivic Cohomology
Lecture Notes on Motivic Cohomology - 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 Lecture Notes on Motivic Cohomology write by Carlo Mazza. This book was released on 2006. Lecture Notes on Motivic Cohomology available in PDF, EPUB and Kindle. Provides an account of the triangulated theory of motives. The book's purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology, and Chow groups.
On Some Properties of Motivic Cohomology
On Some Properties of Motivic Cohomology - 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 On Some Properties of Motivic Cohomology write by Bertrand J. Guillou. This book was released on 2008. On Some Properties of Motivic Cohomology available in PDF, EPUB and Kindle.
The Bloch–Kato Conjecture for the Riemann Zeta Function
The Bloch–Kato Conjecture for the Riemann Zeta Function - 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 The Bloch–Kato Conjecture for the Riemann Zeta Function write by John Coates. This book was released on 2015-03-19. The Bloch–Kato Conjecture for the Riemann Zeta Function available in PDF, EPUB and Kindle. There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
