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.
The Hilbert pairing for formal groups over -rings.
The ideal of relations for the ring of invariants of points on the line
The ring of projective invariants of ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point of this paper that, unlike its close relative the ring of invariants of unordered points, this ring can be completely and simply described. In 1894 Kempe found generators for this ring, thereby proving the First Main Theorem for it (in the terminology introduced by Weyl). In this paper we compute...
The incidence class and the hierarchy of orbits
R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ . Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition (positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity...
The index of centralizers of elements of reductive Lie algebras.
The Invariants of Unipotent Radicals of Parabolic Subgroups.
The Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra
There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian – the Jacobian conjecture claims that the Jacobian...
The kernel of an homomorphism of Harish-Chandra
The Moduli of Weierstrass Fibriations Over P1 .
The moduli scheme M (0, 2, 4) over IP3.