Let G be a group acting on a left or right rigid monoidal triangulated category K which has a Noetherian Balmer spectrum. We prove that the Balmer spectrum of the crossed product category of K by G is homeomorphic to the space of G-prime ideals of K, give a concrete description of this space, and classify the G-invariant thick ideals of K. Under some additional technical conditions, we prove that the Balmer spectrum of the equivariantization of K by G is also homeomorphic to the space of G-prime ideals. Examples of stable categories of finite tensor categories and perfect derived categories of coherent sheaves on Noetherian schemes are used to illustrate the theory.
1
Shanghai University, P. R. China
2
University of California, Los Angeles, USA
Hongdi Huang; Kent B. Vashaw. Group actions on monoidal triangulated categories and Balmer spectra. Documenta mathematica, Tome 30 (2025) no. 5, pp. 1055-1083. doi: 10.4171/dm/1016
@article{10_4171_dm_1016,
author = {Hongdi Huang and Kent B. Vashaw},
title = {Group actions on monoidal triangulated categories {and~Balmer} spectra},
journal = {Documenta mathematica},
pages = {1055--1083},
year = {2025},
volume = {30},
number = {5},
doi = {10.4171/dm/1016},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/1016/}
}
TY - JOUR
AU - Hongdi Huang
AU - Kent B. Vashaw
TI - Group actions on monoidal triangulated categories and Balmer spectra
JO - Documenta mathematica
PY - 2025
SP - 1055
EP - 1083
VL - 30
IS - 5
UR - http://geodesic.mathdoc.fr/articles/10.4171/dm/1016/
DO - 10.4171/dm/1016
ID - 10_4171_dm_1016
ER -
%0 Journal Article
%A Hongdi Huang
%A Kent B. Vashaw
%T Group actions on monoidal triangulated categories and Balmer spectra
%J Documenta mathematica
%D 2025
%P 1055-1083
%V 30
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/1016/
%R 10.4171/dm/1016
%F 10_4171_dm_1016
