تقرير
Hermitian K-theory via oriented Gorenstein algebras
| العنوان: | Hermitian K-theory via oriented Gorenstein algebras |
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| المؤلفون: | Hoyois, Marc, Jelisiejew, Joachim, Nardin, Denis, Yakerson, Maria |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Algebraic Topology, Mathematics - K-Theory and Homology |
| الوصف: | 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. Comment: 30 pages. v4: final version, to appear in J. reine angew. Math. v3: minor changes. v2: Added section 4 on complexity theory |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2103.15474 |
| رقم الأكسشن: | edsarx.2103.15474 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |