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Krull-Schmidt reduction of principal bundles in arbitrary characteristic. (English) Zbl 1097.14012

Summary: Let \(M\) be an irreducible projective variety defined over an algebraically closed field \(k\), and let \(E_G\) be a principal \(G\)-bundle over \(M\), where \(G\) is a connected reductive linear algebraic group defined over \(k\). We show that for \(E_G\) there is a naturally associated conjugacy class of Levi subgroups of \(G\). Given a Levi subgroup \(H\) in this conjugacy class, the principal \(G\)-bundle \(E_G\) admits a reduction of structure group to \(H\). Furthermore, this reduction is unique up to an automorphism of \(E_G\).

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14L10 Group varieties
14L30 Group actions on varieties or schemes (quotients)
14D20 Algebraic moduli problems, moduli of vector bundles
14H60 Vector bundles on curves and their moduli
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References:

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[4] Balaji, V.; Biswas, I.; Nagaraj, D. S., Ramified \(G\)-bundles as parabolic bundles, J Ramanujan Math Soc, 18, 123-138 (2003) · Zbl 1095.14032
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