• Corpus ID: 232404123

Hermitian K-theory via oriented Gorenstein algebras

  title={Hermitian K-theory via oriented Gorenstein algebras},
  author={Marc Hoyois and Joachim Jelisiejew and Denis Nardin and Maria Yakerson},
  journal={arXiv: Algebraic Geometry},
We show that hermitian K-theory is universal among generalized motivic cohomology theories with transfers along finite Gorenstein morphisms with trivialized dualizing sheaf. As an application, we obtain a Hilbert scheme model for hermitian K-theory as a motivic space. We also give an application to computational complexity: we prove that 1-generic minimal border rank tensors degenerate to the big Coppersmith-Winograd tensor. 
5 Citations
Secant varieties and the complexity of matrix multiplication
. This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand
Introduction to Framed Correspondences
We give an overview of the theory of framed correspondences in motivic homotopy theory. Motivic spaces with framed transfers are the analogue in motivic homotopy theory of E ∞ -spaces in classical
The very effective covers of KO and KGL over Dedekind schemes
We answer a question of Hoyois–Jelisiejew–Nardin–Yakerson regarding framed models of motivic connective K-theory spectra over Dedekind schemes. That is, we show that the framed suspension spectrum of
Generalized cohomology theories for algebraic stacks
We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck’s six operations. Objects in this


Geometric models for higher Grothendieck–Witt groups in $$\mathbb {A}^1$$A1-homotopy theory
We show that the higher Grothendieck–Witt groups, a.k.a. algebraic hermitian $$K$$K-groups, are represented by an infinite orthogonal Grassmannian in the $$\mathbb {A}^1$$A1-homotopy category of
Components and singularities of Quot schemes and varieties of commuting matrices
Abstract We investigate the variety of commuting matrices. We classify its components for any number of matrices of size at most 7. We prove that starting from quadruples of 8×8{8\times 8} matrices,
Stable moduli spaces of hermitian forms
We prove that Grothendieck-Witt spaces of Poincar\'e categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Karoubi's classical
Hermitian K-theory for stable $\infty$-categories I: Foundations
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable $\infty$-categories. Our perspective yields solutions to a variety of classical
Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity
We define Grothendieck-Witt spectra in the setting of Poincare $\infty$-categories and show that they fit into an extension with a L- and an L-theoretic part. As consequences we deduce localisation
Cancellation theorem for motivic spaces with finite flat transfers
We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In
η$\eta$ ‐Periodic motivic stable homotopy theory over Dedekind domains
We construct well‐behaved extensions of the motivic spectra representing generalized motivic cohomology and connective Balmer–Witt K$K$ ‐theory (among others) to mixed characteristic Dedekind schemes
The Hilbert scheme of infinite affine space and algebraic K-theory
We study the Hilbert scheme $\mathrm{Hilb}_d(\mathbb{A}^\infty)$ from an $\mathbb{A}^1$-homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilbert scheme
We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler
On the infinite loop spaces of algebraic cobordism and the motivic sphere
We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times