Étale triviality of finite equivariant vector bundles

11 Mar 2021  ·  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 \'etale covering of X is trivial as an H-equivariant bundle...

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Algebraic Geometry Category Theory 32L10, 53C55, 14D21, 16B50