Tamagawa number of reductive algebraic groups
Tame stacks in positive characteristic
We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are étale locally quotient by actions of linearly reductive finite group schemes.
Tate duality and wild ramification.
Tensor Products and Discriminants of Unital Quadratic Forms over Commutative Rings.
The additive group actions on -homology planes
In this article, we prove that a -homology plane with two algebraically independent -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface in the affine -space via a free -action, where is the order of a finite group .
The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
The automorphism group of linear sections of the Grassmannians .
The bar automorphism in quantum groups and geometry of quiver representations
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The canonical combinatorial sheaf associated to an involution of a semisimple adjoint group.
The Capelli identity, the double commutant theorem and multiplicity-free-actions.
The centralizer of a classical group and Bruhat-Tits buildings
Let be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let be the centralizer of a semisimple rational Lie algebra element of We prove that the Bruhat-Tits building of can be affinely and -equivariantly embedded in the Bruhat-Tits building of so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let and be maps from to which preserve the Moy–Prasad filtrations. We prove that...
The Chern character for Lie-Rinehart algebras
Let be a commutative -algebra where is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a -connection. Our result generalizes the classical Chern character from the -theory of to the algebraic De Rham cohomology.
The Chow ring of the stack of cyclic covers of the projective line
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
The cohomology of period domains for reductive groups over finite fields
The correspondence between Barsotti-Tate groups and Kisin modules when
Let be a finite extension over and the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over .
The dimension of some affine Deligne–Lusztig varieties
The Drinfeld Modular Jacobian has connected fibers
We study the integral model of the Drinfeld modular curve for a prime . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of which, after contractions in...
The Ehrhart polynomial of a lattice -simplex.
The equations of conjugacy classes of nilpotent matrices.