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arXiv · 2103.15474

Hermitian K-theory via oriented Gorenstein algebras

Marc Hoyois·Joachim Jelisiejew·Denis Nardin·Maria Yakerson
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Abstract

We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras with trivialized dualizing sheaf. We deduce that hermitian K-theory is universal among generalized motivic cohomology theories with transfers along oriented finite Gorenstein morphisms. 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.

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Marc Hoyois, Joachim Jelisiejew, Denis Nardin, Maria Yakerson. 2021-03-29. Hermitian K-theory via oriented Gorenstein algebras. https://arxiv.org/abs/2103.15474

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