29 citations · 138 across the 15 of their papers we have counts for
18 papers
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…
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…
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 de…
Hermitian K-theory for stable -categories I: Foundations
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable -categories. Our perspective yields solutions to a varie…
Milnor-Witt Motives
Tom Bachmann, Baptiste Calmès, Frédéric Déglise +2
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our defin…
A comparison theorem for MW-motivic cohomology
Baptiste Calmès, Jean Fasel
We prove that for a finitely generated field over an infinite perfect field k, and for any integer n, the (n,n)-th MW-motivic cohomology group identifies with the n-th Milnor-Witt…
Formal affine Demazure and Hecke algebras of Kac-Moody root systems
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extend…
Relative equivariant motives and modules
Baptiste Calmès, Alexander Neshitov, Kirill Zainoulline
We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. W…
Finite Chow-Witt correspondences
Baptiste Calmès, Jean Fasel
We introduce the category of finite Chow-Witt correspondences over a perfect field k of characteristic not 2. We then use them to define bigraded generalized motivic cohomology gro…
Equivariant oriented cohomology of flag varieties
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
Given an equivariant oriented cohomology theory , a split reductive group , a maximal torus in , and a parabolic subgroup containing , we explain how the -eq…
Push-pull operators on the formal affine Demazure algebra and its dual
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the…
A coproduct structure on the formal affine Demazure algebra
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
In the present paper we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology t…
Bases of total Witt groups and lax-similitude
Paul Balmer, Baptiste Calmès
We explain how to work with total Witt groups, more specifically, how to circumvent the classical embarrassment of making choices for line bundles up to isomorphisms and up to squa…
Invariants, torsion indices and oriented cohomology of complete flags
Baptiste Calmès, Victor Petrov, Kirill Zainoulline
In the present notes we generalize the classical work of Demazure [Invariants symétriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and form…
Witt groups of Grassmann varieties
Paul Balmer, Baptiste Calmès
We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis fo…
Geometric description of the connecting homomorphism for Witt groups
Paul Balmer, Baptiste Calmès
We give a geometric setup in which the connecting homomorphism in the localization long exact sequence for Witt groups decomposes as the pull-back to the exceptional fiber of a sui…
Tensor-triangulated categories and dualities
Baptiste Calmès, Jens Hornbostel
In a triangulated symmetric monoidal closed category, there are natural dualities induced by the internal Hom. Given a monoidal functor f^* between two such catgories and adjoint c…
Push-forwards for Witt groups of schemes
Baptiste Calmès, Jens Hornbostel
We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-tri…