A lower bound on the essential dimension of PGL₄ in characteristic 2

2014/11/22 by Sanghoon Baek, Baek, Sanghoon
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1411.6089

openalex publication_date 2014/11/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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 ed(PGL₄)≥ 4 over a field of characteristic 2.

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