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Minimal Trivializing Isogenies of 𝔾m-gerbes over Abelian Varieties and Period-Index Problem
Abstract
For an abelian variety X and α∈ Br(X), we propose a new invariance IndSH(α) that refines the known period index relations. It is closely related to the geometry of 𝒳, the 𝔾m-gerbe over X that corresponds to α: we study the minimal trivializing isogenies for 𝒳 via its μn-lifts and the 1−twisted semi-homogeneous vector bundles on 𝒳. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.
Related
- Derived equivalences and isogenies of supersingular abelian varieties
- Small degree isogenies between conjugate principally polarized superspecial abelian surfaces
- Dynamical degrees of automorphisms on abelian varieties
- A holomorphic (2, 2)-Theorem for Abelian varieties of CM-type
- Arithmetic jet spaces and the unramified Zilber--Pink conjecture for subvarieties of abelian varieties
BibTeX
@misc{li2026minimal,
title = {{Minimal Trivializing Isogenies of $\mathbbG_m$-gerbes over Abelian Varieties and Period-Index Problem}},
author = {Ruoxi Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.30530},
eprint = {2605.30530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30530},
}
RIS
TY - UNPB
TI - Minimal Trivializing Isogenies of 𝔾_m-gerbes over Abelian Varieties and Period-Index Problem
AU - Ruoxi Li
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2605.30530
UR - https://arxiv.org/abs/2605.30530
AB - For an abelian variety X and α∈ 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 𝒳, the 𝔾_m-gerbe over X that corresponds to α: we study the minimal trivializing isogenies for 𝒳 via its μ_n-lifts and the 1−twisted semi-homogeneous vector bundles on 𝒳. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.
ER -