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arXiv · 1308.3078

Affine Grassmannians of group schemes and exotic principal bundles over A^1

Roman Fedorov
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Abstract

Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this end we define affine Grassmannians for group schemes and study their Bruhat decompositions for semi-simple group schemes. We also give examples of principal G-bundles over A^1_U with split G such that the bundles are not isomorphic to pull-backs from U.

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Roman Fedorov. 2016-11-13. Affine Grassmannians of group schemes and exotic principal bundles over A^1. https://doi.org/10.1353/ajm.2016.0036

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