Cdh Descent for Homotopy Hermitian $K$-Theory of Rings with Involution

Autor:	Carmody, Daniel
Rok vydání:	2020
Předmět:	Mathematics - K-Theory and Homology Mathematics - Algebraic Geometry Mathematics - Algebraic Topology
Zdroj:	Doc. Math. 26, 1275-1327 (2021)
Druh dokumentu:	Working Paper
Popis:	We provide a geometric model for the classifying space of automorphism groups of Hermitian vector bundles over a ring with involution $R$ such that $\frac{1}{2} \in R$; this generalizes a result of Schlichting-Tripathi \cite{SchTri}. We then prove a periodicity theorem for Hermitian $K$-theory and use it to construct an $E_\infty$ motivic ring spectrum $\mathbf{KR}^{\mathrm{alg}}$ representing homotopy Hermitian $K$-theory. From these results, we show that $\mathbf{KR}^{\mathrm{alg}}$ is stable under base change, and cdh descent for homotopy Hermitian $K$-theory of rings with involution is a formal consequence. Comment: 34 pages: Final version - removed unnecessary hypothesis in theorem 5.1
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.09124 Zobrazit plný text záznamu View this record from Arxiv