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arXiv · 1601.00590

Spinors and essential dimension

Skip Garibaldi·Robert M. Guralnick
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Abstract

We prove that spin groups act generically freely on various spinor modules, in the sense of group schemes and in a way that does not depend on the characteristic of the base field. As a consequence, we extend the surprising calculation of the essential dimension of spin groups and half-spin groups in characteristic zero by Brosnan--Reichstein--Vistoli (Annals of Math., 2010) and Chernousov--Merkurjev (Algebra & Number Theory, 2014) to fields of characteristic different from 2.

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Skip Garibaldi, Robert M. Guralnick. 2016-01-04. Spinors and essential dimension. https://doi.org/10.1112/s0010437x16008162

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