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Pullback of principal bundles along proper morphisms
Indranil Biswas, Peter O'Sullivan
We study the behaviour of principal bundles under pullback along proper surjective morphisms of either schemes over an algebraically closed field of characteristic 0 or complex ana…
Étale triviality of finite equivariant vector bundles
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 consta…
Principal bundles under reductive groups
Peter O'Sullivan
Let be a field of characteristic . We consider principal bundles over a -scheme with reductive structure group (not necessarily of finite type). It is showm in particular…
A finiteness theorem for algebraic cycles
Peter O'Sullivan
Let X be a smooth projective variety. Starting with a finite set of cycles on powers X^m of X, we consider the Q-vector subspaces of the Q-linear Chow groups of the X^m obtained by…
Algebraic cycles on an abelian variety
Peter O'Sullivan
It is shown that to every Q-linear cycle \barαmodulo numerical equivalence on an abelian variety A there is canonically associated a Q-linear cycle αmodulo rational equivalence on…