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.
The First Cohomology Group of a Line Bundle on G/B.
The formal completion of the Néron model of J0(p).
For any prime number p > 3 we compute the formal completion of the Néron model of J0(p) in terms of the action of the Hecke algebra on the Z-module of all cusp forms (of weight 2 with respect to Γ0(p)) with integral Fourier development at infinity.
The fundamental groupoid scheme and applications
We define a linear structure on Grothendieck’s arithmetic fundamental group of a scheme defined over a field of characteristic 0. It allows us to link the existence of sections of the Galois group to with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering of the affine...
The Fundamental Group-Scheme of an Abelian Variety.
The Galois-module structure of the space of holomorphic differentials of a curve.
The Geometry of Representations of Am .
The global structure of moduli spaces of polarized -divisible groups.
The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits
The Grothendieck-Riemann-Roch theorem for group scheme actions
The Hasse-Witt Matrix of a Formal Group.