Noncommutative Motives is popular PDF and ePub book, written by Gonçalo Tabuada in 2015-09-21, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Noncommutative Motives can be Read Online from any device for your convenience.
Noncommutative Motives Book PDF Summary
The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
Detail Book of Noncommutative Motives PDF
- Author : Gonçalo Tabuada
- Release : 21 September 2015
- Publisher : American Mathematical Soc.
- ISBN : 9781470423971
- Genre : Mathematics
- Total Page : 127 pages
- Language : English
- PDF File Size : 20,9 Mb
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