## Indranil Biswas ; Peter O'Sullivan - \'Etale triviality of finite equivariant vector bundles

epiga:7275 - Épijournal de Géométrie Algébrique, November 19, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.7275
\'Etale triviality of finite equivariant vector bundles

Authors: Indranil Biswas ; Peter O'Sullivan

Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{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.

Volume: Volume 5
Published on: November 19, 2021
Accepted on: November 19, 2021
Submitted on: March 17, 2021
Keywords: Mathematics - Algebraic Geometry,Mathematics - Category Theory,32L10, 53C55, 14D21, 16B50