On a Class of 2-Periodic Cohomology Theories.
On a conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
On a Fermat Equation Arising in the Arithmetic Theory of Function Fields.
On a separation of orbits in the module variety for domestic canonical algebras
Given a pair M,M' of finite-dimensional modules over a domestic canonical algebra Λ, we give a fully verifiable criterion, in terms of a finite set of simple linear algebra invariants, deciding if M and M' lie in the same orbit in the module variety, or equivalently, if M and M' are isomorphic.
On a variation of Mazur's deformation functor
On actions of on algebraic spaces
The main result of the paper says that all schematic points of the source of an action of on an algebraic space are schematic on .
On automorphisms of Enriques surfaces.
On Automorphisms of the Affine Cremona Group
We show that every automorphism of the group of polynomial automorphisms of complex affine -space is inner up to field automorphisms when restricted to the subgroup of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension where all automorphisms are tame: . The methods are different, based on arguments from algebraic group actions.
On canonical and quasi-canonical liftings.
On Certain Representations of Semi-Simple Algebraic Groups and the Arithmetic of the Corresponding Invariants.
On classical invariant theory and binary cubics
Let be a reductive complex algebraic group, and let denote the algebra of invariant polynomial functions on the direct sum of copies of the representations space of . There is a smallest integer such that generators and relations of can be obtained from those of by polarization and restitution for all . We bound and the degrees of generators and relations of , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
On complete orbit spaces of SL(2) actions
On complete orbit spaces of SL(2) actions, II
The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.
On complex affine surfaces with ...-action.
On conjugating representations and adjoint representations of semisimple groups.
On deformation method in invariant theory
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let be a reductive group, an affine -variety and a spherical subgroup. We show that whenever is affine and its semigroup of weights is saturated, the algebra of -invariant regular functions on has a -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of . The deformation method in its usual form, as developed...
On Drinfeld's universal formal group over the p-adic upper half plane.
On Exact Actions of Unipotent Groups.
On existence of double coset varieties
Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible space....
On finite same-invariant linear groups.