Sanghoon Baek: A lower bound on the essential dimension of $\operatorname{\mathbf{PGL}}_{4}$ in characteristic $2$

Submission: 2015, Apr 4

In the present paper, we provide a lower bound of the essential dimension over a field of positive characteristic via Kato's cohomology group, defined by cokernel of a general Artin-Schreier operator. Combining this with Tignol's result on the second trace form of simple algebras of degree $4$, we show that $\operatorname{ed}(\operatorname{\mathbf{PGL}}_{4})\geq 4$ over a field of characteristic $2$.

2010 Mathematics Subject Classification: 11E04, 16H05, 11E72

Keywords and Phrases: Essential dimension, projective linear group, central simple algebra, trace form, Galois cohomology

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