# Hermitian K-theory via oriented Gorenstein algebras

@article{Hoyois2021HermitianKV, title={Hermitian K-theory via oriented Gorenstein algebras}, author={Marc Hoyois and Joachim Jelisiejew and Denis Nardin and Maria Yakerson}, journal={arXiv: Algebraic Geometry}, year={2021} }

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

- Mathematics
- 2022

. 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

- Mathematics
- 2022

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

- Mathematics
- 2022

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…

Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science

- MathematicsDifferential Geometry and its Applications
- 2022

Generalized cohomology theories for algebraic stacks

- Mathematics
- 2021

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…

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