6 papers
Hermitian K-theory for stable -categories III: Grothendieck-Witt groups of rings
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring to the homotopy -orbits of its K-theory and Ranicki's original (non-period…
Trace methods for stable categories I: The linear approximation of algebraic K-theory
Yonatan Harpaz, Thomas Nikolaus, Victor Saunier
We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this se…
Deformation theory and cotangent complex of dg operads
Yonatan Harpaz, Truong Hoang
In the first part, we give an explicit description of the cotangent complex of differential graded (dg) operads, modeled as an operadic infinitesimal bimodule. This leads to a unif…
Stable moduli spaces of hermitian forms
Fabian Hebestreit, Wolfgang Steimle
We prove that Grothendieck-Witt spaces of Poincaré categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Ka…
Hermitian K-theory for stable -categories II: Cobordism categories and additivity
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We define Grothendieck-Witt spectra in the setting of Poincaré -categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we d…
A motivic spectrum representing hermitian K-theory
Baptiste Calmès, Yonatan Harpaz, Denis Nardin
We establish fundamental motivic results about hermitian K-theory without assuming that 2 is invertible on the base scheme. In particular, we prove that both quadratic and symmetri…