 |
Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity
Abstract : We define Grothendieck-Witt spectra in the setting of Poincar\'e $\infty$-categories, show that they fit into an extension with a K- and an L-theoretic part and deduce localisation sequences for Verdier quotients. As special cases we obtain generalisations of Karoubi's fundamental and periodicity theorems for rings in which 2 need not be invertible. A novel feature of our approach is the systematic use of ideas from cobordism theory by interpreting the hermitian Q-construction as an algebraic cobordism category. We also use this to give a new description of the LA-spectra of Weiss and Williams.
https://hal-univ-artois.archives-ouvertes.fr/hal-02941256
Contributor : Baptiste Calmès Connect in order to contact the contributor
Submitted on : Wednesday, September 16, 2020 - 9:17:35 PM
Last modification on : Wednesday, November 3, 2021 - 6:19:57 AM
Contributor : Baptiste Calmès Connect in order to contact the contributor
Submitted on : Wednesday, September 16, 2020 - 9:17:35 PM
Last modification on : Wednesday, November 3, 2021 - 6:19:57 AM
Links full text
