Geodesic
Cdh descent for homotopy Hermitian $K$-theory of rings with involution
Documenta mathematica, Tome 26 (2021), pp. 1275-1327 Cet article a éte moissonné depuis la source EMS Press

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We provide a geometric model for the classifying space of automorphism groups of Hermitian vector bundles over a ring with involution R such that 21​∈R; this generalizes a result of M. Schlichting and 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∞​ motivic ring spectrum KRalg representing homotopy Hermitian K-theory. From these results, we show that KRalg is stable under base change, and cdh descent for homotopy Hermitian K-theory of rings with involution is a formal consequence.
DOI : 10.4171/dm/842
Classification : 14F42, 19D25
Mots-clés : algebraic K-theory, motivic homotopy theory 
@article{10_4171_dm_842,
     author = {Daniel Carmody},
     title = {Cdh descent for homotopy {Hermitian} $K$-theory of rings with involution},
     journal = {Documenta mathematica},
     pages = {1275--1327},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/842},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/842/}
}
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Daniel Carmody. Cdh descent for homotopy Hermitian $K$-theory of rings with involution. Documenta mathematica, Tome 26 (2021), pp. 1275-1327. doi: 10.4171/dm/842

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