Galois characters associated to formal -modules
Galois covers between surfaces
We give a classification of finite group actions on a surface giving rise to quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.
Galois descent and cohomology for algebraic groups.
Galois extensions of height-one commuting dynamical systems
We consider a dynamical system consisting of a pair of commuting power series under composition, one noninvertible and another nontorsion invertible, of height one with coefficients in the -adic integers. Assuming that each point of the dynamical system generates a Galois extension over the base field, we show that these extensions are in fact abelian, and, using results from the theory of the field of norms, we also show that the dynamical system must include a torsion series. From an earlier...
Galois Properties of Torsion Points on Abelian Varieties.
Gaussian Maps and Tensor products of irreducible representations.
Gauss-Manin stratification and stratified fundamental group schemes
We define the zero-th Gauss-Manin stratification of a stratified bundle with respect to a smooth morphism and use it to study the homotopy sequence of stratified fundamental group schemes.
General linear and functor cohomology over finite fields.
Generalized quivers associated to reductive groups
We generalize the definition of quiver representation to arbitrary reductive groups. The classical definition corresponds to the general linear group. We also show that for classical groups our definition gives symplectic and orthogonal representations of quivers with involution inverting the direction of arrows.
Generalized support varieties for finite group schemes.
Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of -kernel.
Geometric Invariant Theory and Generalized Eigenvalue Problem II
Let be a connected reductive subgroup of a complex connected reductive group . Fix maximal tori and Borel subgroups of and . Consider the cone generated by the pairs of strictly dominant characters such that is a submodule of . We obtain a bijective parametrization of the faces of as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.
Geometric invariant theory for general algebraic groups
Geometry of an étale covering of the -adic upper half plane
We describe the rigid geometry of the first layer in the tower of coverings of the -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.
Geometry of infinitesimal group schemes.
Geometry of modules over tame quasi-tilted algebras
GIT quotients of products of projective planes
Glatte Einbettungen von G-U .
Global Moduli for Surfaces of General Type.
Good moduli spaces for Artin stacks
We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford’s geometric invariant theory and tame stacks.