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- W3105508311 abstract "Let ${bf G}$ be a simple simply-connected group scheme over a regular local scheme $U$. Let ${mathcal E}$ be a principal ${bf G}$-bundle over ${Bbb A}^1_U$ trivial away from a subscheme finite over $U$. We show that ${mathcal E}$ 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 ${bf G}$-bundles over ${Bbb A}^1_U$ with split ${bf G}$ such that the bundles are not isomorphic to pullbacks from $U$." @default.
- W3105508311 created "2020-11-23" @default.
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- W3105508311 date "2016-01-01" @default.
- W3105508311 modified "2023-10-17" @default.
- W3105508311 title "Affine Grassmannians of group schemes and exotic principal bundles over ${Bbb A}^1$" @default.
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- W3105508311 doi "https://doi.org/10.1353/ajm.2016.0036" @default.
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