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Motives and Algebraic Cycles

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 946/5 ( reviews)

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Book Synopsis Motives and Algebraic Cycles by : Rob de Jeu

Download or read book Motives and Algebraic Cycles written by Rob de Jeu. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic $K$-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.

Algebraic Cycles and Motives: Volume 1

2007-05-03 Mathematics
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Release : 2007-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 740/5 ( reviews)

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Book Synopsis Algebraic Cycles and Motives: Volume 1 by : Jan Nagel

Download or read book Algebraic Cycles and Motives: Volume 1 written by Jan Nagel. This book was released on 2007-05-03. Available in PDF, EPUB and Kindle. Book excerpt: This 2007 book is a self-contained account of the subject of algebraic cycles and motives.

Mixed Motives and Algebraic K-Theory

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 419/5 ( reviews)

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Book Synopsis Mixed Motives and Algebraic K-Theory by : Uwe Jannsen

Download or read book Mixed Motives and Algebraic K-Theory written by Uwe Jannsen. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.

Motivic Homotopy Theory

2007-07-11 Mathematics
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Release : 2007-07-11
Genre : Mathematics
Kind : eBook
Book Rating : 972/5 ( reviews)

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Book Synopsis Motivic Homotopy Theory by : Bjorn Ian Dundas

Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas. This book was released on 2007-07-11. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

Motives

1994-02-28 Mathematics
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Release : 1994-02-28
Genre : Mathematics
Kind : eBook
Book Rating : 987/5 ( reviews)

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Book Synopsis Motives by :

Download or read book Motives written by . This book was released on 1994-02-28. Available in PDF, EPUB and Kindle. Book excerpt: 'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.

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