Minimal Trivializing Isogenies of $\mathbb{G}_m$-gerbes over Abelian Varieties and Period-Index Problem
Year: 2026
Type: preprint
Abstract: For an abelian variety $X$ and $α\in Br(X)$, we propose a new invariance $Ind_{SH}(α)$ that refines the known period index relations. It is closely related to the geometry of $\mathcal{X}$, the $\mathbb{G}_m$-gerbe over $X$ that corresponds to $α$: we study the minimal trivializing isogenies for $\mathcal{X}$ via its $μ_n$-lifts and the $1-$twisted semi-homogeneous vector bundles on $\mathcal{X}$. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.
Source: arXiv (Cornell University)
Author: Li, Ruoxi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163009252