Twisted k-theory in motivic homotopy theory
WebApr 10, 2024 · Abstract: In this talk, we will speak about algebraic K-theory of vector bundles twisted by a Brauer class, and its place in motivic homotopy theory. In particular, we will discuss a new approach to the motivic spectral sequence for twisted K-theory, constructed earlier by Bruno Kahn and Marc Levine. WebWe show that the spectrum of Kontsevich’s algebra of formal periods is a torsor under the motivic Galois group for mixed motives over Q. This assertion is stated without proof by Kontsevich ([Ko] Theorem 6) and originally due to Nori. In a series of appendices, we also provide the necessary details on Nori’s category of motives (see the survey [Le]).
Twisted k-theory in motivic homotopy theory
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WebOct 18, 2024 · A bstract . In this paper, we study twisted algebraic K-theory from a motivic viewpoint. For a smooth variety X over a field of characteristic zero and an Azumaya … WebSep 10, 2024 · In this talk, we will speak about algebraic K-theory of vector bundles twisted by a Brauer class, and its place in motivic homotopy theory. In particular, we will discuss …
WebSome topics in the theory of Tannakian categories and applications to motives and motivic Galois groups ... Alexander A. Height pairing between algebraic cycles, K-theory, arithmetic and geometry (Moscow, ... Fabien; Voevodsky, Vladimir A 1-homotopy theory of schemes, Publ. Math., Inst. Hautes Étud. Sci. (1999) no. 90, ... WebTopic: Motivic homotopy theory involves the study of algebraic varieties and schemes using methods not only from algebraic geometry, but also from algebraic topology. A basic idea is to use techniques from homotopy theory, such as the construction of homotopy groups and the use of homotopical invariants, to investigate topological and geometric properties of …
Web2. Stable A1-homotopy theory 7 2.1. The stabilization procedure and spectra 7 2.2. A (brief) summary of the six functors formalism 10 3. Algebraic K-theory and Beilinson motives 11 3.1. Representability algebraic K-theory 11 3.2. Beilinson motivic cohomology 13 3.3. Beilinson motives 15 4. Conclusion 17 References 17 basic algebraic geometry ... Webtwisted K-theory as an extension ofthe twisted Grassmannian bythe sheaf of“twisted integers”. This leads to a proof of cdh descent and Milnor excision for twisted homotopy …
WebAug 29, 2010 · The proof employs an Adams Hopf algebroid and a tri-graded Tor-spectral sequence for motivic twisted K-theory. By adopting the notion of an E-infinity ring …
WebAug 29, 2010 · The proof employs an Adams Hopf algebroid and a tri-graded Tor-spectral sequence for motivic twisted K-theory. By adopting the notion of an E-infinity ring spectrum to the motivic homotopy theoretic setting, we construct spectral sequences relating motivic (co)homology groups to twisted K-groups. specific motor innervation of nerve vWebThe electronic Computational Homotopy Theory Seminar is an online international research seminar. Topics include any part of homotopy theory that has a computational flavor, including but not limited to stable homotopy theory, unstable homotopy theory, chromatic homotopy theory, equivariant homotopy theory, motivic homotopy theory, and K-theory. specific narrowed down topicWebThis paper sets out basic properties of motivic twisted K –theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K –theory is defined in … specific objective of financial reporting