95 citations · 132 across the 14 of their papers we have counts for
15 papers
Symmetric versus genuine symmetric forms in Hermitian K-theory
Marco Schlichting
We show that for finite dimensional regular Noetherian rings that contain a field or are smooth over a Dedekind domain, the comparison map from the Hermitian K-theory of genuine sy…
Higher -theory of forms III: from chain complexes to derived categories
Daniel Marlowe, Marco Schlichting
We exhibit a canonical equivalence between the hermitian -theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincaré -category,…
Higher K-theory of forms II. From exact categories to chain complexes
Marco Schlichting
We prove basic statements about the Hermitian K-theory of exact form categories with weak equivalences. Notably, we extend a quadratic functor with values in abelian groups from an…
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…
On the Homological Stability of Orthogonal and Spin Groups
Marco Schlichting, Sunny Sood
We improve homological stability ranges for the orthogonal group, special orthogonal group, elementary orthogonal group and the spin group over a commutative local ring with in…
On the Homology stability range for symplectic groups
Marco Schlichting
We improve, by a factor of 2, known homology stability ranges for the integral homology of symplectic groups over commutative local rings with infinite residue field and show that…
The third homology of symplectic groups and algebraic K-theory
Marco Schlichting, Husney Parvez Sarwar
We improve the homology stability range for the 3rd integral homology of symplectic groups over commutative local rings with infinite residue field. As an application, we show that…
Grothendieck-Witt groups of some singular schemes
Max Karoubi, Marco Schlichting, Charles Weibel
We establish some structural results for the Witt and Grothendieck-Witt groups of schemes over , including homotopy invariance for Witt groups and a formula for th…
The Witt group of real algebraic varieties
Max Karoubi, Marco Schlichting, Charles Weibel
Let be an algebraic variety over . The purpose of this paper is to compare its algebraic Witt group with a new topological invariant , base…
Euler class groups, and the homology of elementary and special linear groups
Marco Schlichting
We prove homology stability for elementary and special linear groups over rings with many units improving known stability ranges. Our result implies stability for unstable Quillen…
Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory
Marco Schlichting, Girja Shanker Tripathi
We show that the higher Grothendieck-Witt groups, a.k.a. algebraic hermitian K-groups, are represented by an infinite orthogonal Grassmannian in the A1-homotopy category of smooth…
Hermitian K-theory, derived equivalences and Karoubi's Fundamental Theorem
Marco Schlichting
Within the framework of dg categories with weak equivalences and duality that have uniquely 2-divisible mapping complexes, we show that higher Grothendieck-Witt groups (aka. hermit…
The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory
A. J. Berrick, M. Karoubi, M. Schlichting +1
Let X be a noetherian scheme of finite Krull dimension, having 2 invertible in its ring of regular functions, an ample family of line bundles, and a global bound on the virtual mod…
The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes
Marco Schlichting
We prove localization and Zariski-Mayer-Vietoris for higher Grothendieck-Witt groups, alias hermitian -groups, of schemes admitting an ample family of line-bundles. No assumptio…
Cyclic homology, cdh-cohomology and negative K-theory
G. Cortiñas, C. Haesemeyer, M. Schlichting +1
We prove a blow-up formula for cyclic homology which we use to show that infinitesimal -theory satisfies -descent. Combining that result with some computations of the …