A new fibre sequence relates classical Grothendieck-Witt groups to K-theory orbits and symmetric L-theory, enabling removal of the 2-unit assumption and resolution of multiple open problems for Dedekind rings and number rings.
A Grothendieck-Witt space for stable infinity categories with duality
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We construct a Grothendieck-Witt space for any stable infinity category with duality. If we apply our construction to perfect complexes over a commutative ring in which 2 is invertible we recover the classical Grothendieck-Witt space. Our Grothendieck-Witt space is a grouplike E-infinity space which is part of a genuine C_2-spectrum, the connective real K-theory spectrum.
fields
math.KT 1years
2020 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Hermitian K-theory for stable $\infty$-categories III: Grothendieck-Witt groups of rings
A new fibre sequence relates classical Grothendieck-Witt groups to K-theory orbits and symmetric L-theory, enabling removal of the 2-unit assumption and resolution of multiple open problems for Dedekind rings and number rings.