38 citations · 125 across the 18 of their papers we have counts for
9 papers · 1 filter
On the -theory of pushouts
Markus Land, Georg Tamme
We reveal a relation between the behaviour of localizing invariants on pushouts and on pullbacks of ring spectra. More concretely, we show that the failure of sending a pus…
L-theory of -algebras
Markus Land, Thomas Nikolaus, Marco Schlichting
We establish a formula for the L-theory spectrum of real -algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all prev…
Gabber rigidity in hermitian K-theory
Markus Land
We note that Gabber's rigidity theorem for the algebraic K-theory of henselian pairs also holds true for hermitian K-theory with respect to arbitrary form parameters.
Remarks on chromatically localised hermitian K-theory
Markus Land
We describe chromatic localisations of genuine L-spectra of discrete rings and deduce that the purity property of -local -theory of rings established by Bhatt-Clausen-Math…
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…
Purity in chromatically localized algebraic -theory
Markus Land, Akhil Mathew, Lennart Meier +1
We prove a purity property in telescopically localized algebraic -theory of ring spectra: For , the -localization of only depends on the $T(0)\oplus \dots…
On the K-theory of pullbacks
Markus Land, Georg Tamme
To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic -theory. The construction of this new ring sp…
The Analytical Assembly Map and Index Theory
Markus Land
In this paper we study the index theoretic interpretation of the analytical assembly map that appears in the Baum-Connes conjecture. In its general form it may be constructed using…