Étale triviality of finite equivariant vector bundles
Épijournal de Géométrie Algébrique, Tome 5 (2021)
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Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_red of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle E over X is $H$-finite, meaning f_1(E)= f_2(E) as H-equivariant bundles for two distinct polynomials f_1 and f_2 whose coefficients are nonnegative integers, if and only if the pullback of E along some H-equivariant finite étale covering of X is trivial as an H-equivariant bundle.
@article{10_46298_epiga_2021_7275,
author = {Biswas, Indranil and O'Sullivan, Peter},
title = {\'Etale triviality of finite equivariant vector bundles},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {5},
year = {2021},
doi = {10.46298/epiga.2021.7275},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.7275/}
}
TY - JOUR AU - Biswas, Indranil AU - O'Sullivan, Peter TI - Étale triviality of finite equivariant vector bundles JO - Épijournal de Géométrie Algébrique PY - 2021 VL - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.7275/ DO - 10.46298/epiga.2021.7275 LA - en ID - 10_46298_epiga_2021_7275 ER -
%0 Journal Article %A Biswas, Indranil %A O'Sullivan, Peter %T Étale triviality of finite equivariant vector bundles %J Épijournal de Géométrie Algébrique %D 2021 %V 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.7275/ %R 10.46298/epiga.2021.7275 %G en %F 10_46298_epiga_2021_7275
Biswas, Indranil; O'Sullivan, Peter. Étale triviality of finite equivariant vector bundles. Épijournal de Géométrie Algébrique, Tome 5 (2021). doi: 10.46298/epiga.2021.7275
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