The essential $2$-dimension of the linear groups

Abstract

In this paper, we compute the essential $2$-dimension when the defining prime is odd of the general linear groups, the projective general linear groups, the special linear groups when $n$ is odd or $n=2$, as well as the special linear groups and quotients of it (such as the projective special linear groups) in the case case $q\equiv 1\mathrm{mod}4$, $s=v_2(q-1)$, and $\Gamma =\text{Gal}(k({\zeta }_{2^s})/k)$ is trivial.

arXiv admin note: text overlap with arXiv:2109.02698 and arXiv:2204.13227