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.

Series: Lecture Notes in Mathematics (Book 1400).

Find all the books, read about the author, and more. Are you an author? Learn about Author Central. Uwe Jannsen (Author). ISBN-13: 978-0387522609. Series: Lecture Notes in Mathematics (Book 1400). Paperback: 246 pages. Publisher: Springer Verlag (June 1, 1990).

Lecture Notes in Mathematics. Mixed Motives and Algebraic K-Theory. price for USA in USD (gross). ISBN 978-3-540-46941-4. Digitally watermarked, DRM-free. Included format: PDF. ebooks can be used on all reading devices. Immediate eBook download after purchase.

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 Poincar? 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.

oceedings{Jannsen1990MixedMA, title {Mixed Motives and Algebraic K-Theory}, author {Uwe Jannsen}, year {1990} . Mixed motives for absolute hodge cycles. Algebraic cycles, K-theory, and extension classes.

oceedings{Jannsen1990MixedMA, title {Mixed Motives and Algebraic K-Theory}, author {Uwe Jannsen}, year {1990} }. Uwe Jannsen. K-theory and ?-adic cohomology.

Mixed Motives and Algebraic K-Theory. Part of the Lecture Notes in Mathematics book series (LNM, volume 1400). 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.

Part II Arithmetic Theory: Galois Cohomology. Cohomology of Local Fields

4 under arithmetic assumptions. Part II Arithmetic Theory: Galois Cohomology. Cohomology of Local Fields. Cohomology of Global Fields. Let X be a complex algebraic manifold of dimension n+1 embedded in a sufficiently higher dimensional complex projective space, and Y a generic hyperplane section of X. We describe the mixed Hodge structure on H^p(X-Y,C) and the Hodge filtration of the middle primitive cohomology group H^n(Y,C) 0 of Y in terms of rational integrals on. X. (Key words: Primitive cohomology, Rational integral of the.

A generalization of the various cohomology theories of algebraic varieties. The theory of motives systematically generalizes the idea of using the Jacobi variety of an algebraic curve as a replacement for the cohomology group in the classical theory. The theory of motives systematically generalizes the idea of using the Jacobi variety of an algebraic curve as a replacement for the cohomology group in the classical theory of correspondences, and the use of this theory in the study of the zeta-function of a curve over a finite field

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory . Motivic cohomology itself had been invented before the creation of mixed motives by means of algebraic K-theory.

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically, a 'motif' is the 'cohomology essence' of a variety.

Jannsen, . Mixed motives and algebraic K-theory, Lecture Notes in Mathematics, vol. 1400 (Springer . 1400 (Springer, Berlin, 1990). Lichtenbaum, . Values of zeta-functions at nonnegative integers, in Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), Lecture Notes in Mathematics, vol. 1068 (Springer, Berlin, 1984), 127–138. Grothendieck, . Cohomologie ℓ-adique et fonctions L, Lecture Notes in Mathematics, vol. 589 (Springer, Berlin, 1977); Séminaire de Géométrie Algébrique du Bois–Marie 1965–66 (SGA 5). Suslin, A. and Voevodsky, . Singular homology of abstract algebraic varieties, Invent.