Geodesic
Cdh descent for homotopy Hermitian $K$-theory of rings with involution
Documenta mathematica, Tome 26 (2021), pp. 1275-1327.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 \textit{M. Schlichting} and \textit{G. S. Tripathi} [Math. Ann. 362, No. 3--4, 1143--1167 (2015; Zbl 1331.14028)]. We then prove a periodicity theorem for Hermitian $K$-theory and use it to construct an $E_\infty$ motivic ring spectrum $\mathbf{KR}^{\text{alg}}$ representing homotopy Hermitian $K$-theory. From these results, we show that $\mathbf{KR}^{\text{alg}}$ is stable under base change, and cdh descent for homotopy Hermitian $K$-theory of rings with involution is a formal consequence.
Classification : 19D25, 14F42
Keywords: algebraic \(K\)-theory, motivic homotopy theory 
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     author = {Carmody, Daniel},
     title = {Cdh descent for homotopy {Hermitian} {\(K\)-theory} of rings with involution},
     journal = {Documenta mathematica},
     pages = {1275--1327},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a22/}
}
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Carmody, Daniel. Cdh descent for homotopy Hermitian \(K\)-theory of rings with involution. Documenta mathematica, Tome 26 (2021), pp. 1275-1327. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a22/