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arXiv · 1801.04784

Triviality properties of principal bundles on singular curves-II

Prakash Belkale·Najmuddin Fakhruddin
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Abstract

For $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\to S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D \subset X$. We show, by constructing explicit examples, that the obstruction is nontrivial if $G$ is not simply connected but it can be made to vanish, if $S$ is the spectrum of a dvr (and some other hypotheses), by a faithfully flat base change. The vanishing of this obstruction is shown to be a sufficient condition for etale local triviality if $S$ is a smooth curve, and the singular locus of $X-D$ is finite over $S$.

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Prakash Belkale, Najmuddin Fakhruddin. 2018-01-15. Triviality properties of principal bundles on singular curves-II. https://arxiv.org/abs/1801.04784

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