Trace theories, Bokstedt periodicity and Bott periodicity

Autor:	Kaledin, D.
Rok vydání:	2020
Předmět:	Mathematics - K-Theory and Homology Mathematics - Algebraic Geometry Mathematics - Algebraic Topology Mathematics - Category Theory
Druh dokumentu:	Working Paper
Popis:	We flesh out the theory of "trace theories" and "trace functors" sketched in arXiv:1308.3743, extend it to a homotopical setting, and prove a reconstruction theorem claiming that a trace theory is completely determined by the associated trace functor. As an application, we consider Topological Hoshschild Homology $THH(A,M)$ of a algebra $A$ over a perfect field of positive characteristic, with coefficients in a bimodule $M$, and prove two comparison results. Firstly, we give a very simple algebraic model for THH in terms of Hochschild-Witt Homology WHH of arXiv:1604.01588 (and we also identify $TP(A)$ with the periodic version $WHP(A)$ of WHH). Secondly, we prove that $THH(A)$ is identified with the zero term of the conjugate filtration on the co-periodic cyclic homology $\overline{HP}(A)$ of arXiv:1509.08784, and the isomorphism sends the Bokstedt periodicity generator to the Bott periodicity generator. We also give an independent proof of Bokstedt periodicity that is somewhat shorter than the usual ones. Comment: LaTeX2e, 210 pages. Minor changes: updated grant acknowledgements, added a couple of small lemmas
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.04279 Zobrazit plný text záznamu View this record from Arxiv