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Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups

Filling Bestvina, Alex Eskin, Kevin Wortman (2013)

Journal of the European Mathematical Society

We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux....

Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular -cohomology of a point. Suppose that G is a complex algebraic group acting algebraically on X . Our main results are the following: if G is semi-simple, then the generic fiber of the quotient map π : X X / / G contains a dense orbit. If G is connected and reductive, then the action has fixed points if dim X / / G 3 .

Flasque resolutions of reductive group schemes

Cristian González-Avilés (2013)

Open Mathematics

We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.

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