On nilpotent automorphism groups of function fields

Abstract: We study the automorphisms of a function field of genus $g\geq 2$ over an algebraically closed field of positive characteristic $p$. More precisely, we show that the order of a nilpotent subgroup $G$ of its automorphism group is bounded by $16(g−1)$ when $G$ is not a $p$-group. We show that if $|G|=16(g−1)$, then $g−1$ is a power of $2$. Furthermore, we provide an infinite family of function fields attaining the bound. This is a joint work with Nurdagül Anbar.

commutative algebraalgebraic geometrynumber theoryrepresentation theory

Audience: advanced learners

UCGEN - Uluslararası Cebirsel GEometri Neşesi

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