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The Virtual Poincaré Polynomials of Homogeneous Spaces
Wiley - Tập 134 - Trang 319-335 - 2002
We factor the virtual Poincaré polynomial of every homogeneous space G/H, where
G is a complex connected linear algebraic group and H is an algebraic subgroup,
as t2u (t2−1)r QG/H(t2) for a polynomial QG/H with nonnegative integer
coefficients. Moreover, we show that QG/H(t2) divides the virtual Poincaré
polynomial of every regular embedding of G/H, if H is connected.
Hecke Algebras and Automorphic Forms
Wiley - Tập 130 - Trang 21-48 - 2002
The goal of this paper is to carry out some explicit calculations of the actions
of Hecke operators on spaces of algebraic modular forms on certain simple
groups. In order to do this, we give the coset decomposition for the supports of
these operators. We present the results of our calculations along with
interpretations concerning the lifting of forms. The data we have obtained is of
interest bot...
Cohomology of Real Diagonal Subspace Arrangements via Resolutions
Wiley - Tập 117 - Trang 107-123 - 1999
We express the cohomology of the complement of a real subspace arrangement of
diagonal linear subspaces in terms of the Betti numbers of a minimal free
resolution. This leads to formulas for the cohomology in some cases, and also to
a cohomology vanishing theorem valid for all arrangements.
Models of Curves and Finite Covers
Wiley - - 1999
Let K be a discrete valuation field with ring of integers O K .Letf : X ! Y be a
finite morphism of curves over K. In this article, we study some possible
relationships between the models over O K of X and of Y. Three such
relationships are listed below. Consider a Galois cover f : X ! Y of degree
prime to the characteristic of the residue field, with branch locus B. We show
that if Y has semi-sta...
Perverse Sheaves on Image Multiple Point Spaces
Wiley - Tập 123 - Trang 117-130 - 2000
Using multiple point spaces some new examples of perverse sheaves on images of
maps are described. Furthermore, suppose $$f:X \to Y$$ is a finite and proper
map of complex analytic manifolds of dimension n and n+1 such that every
multiple point space is nonsingular and has the dimension expected of a generic
map. Then we can describe the composition series for the constant sheaf on the
image in th...
Deformations of Codimension 2 Toric Varieties
Wiley - Tập 123 - Trang 225-241 - 2000
We prove Sturmfels' conjecture that toric varieties of codimension two have no
other flat deformations than those obtained by Gröbner basis theory.
Revêtements des courbes en caractéristique p>0 et ordinarité
Wiley - Tập 123 - Trang 73-88 - 2000
Let X be a proper, smooth, connected curve, defined over an algebraically closed
field of characteristic p>0 and of genus g ≥ 2. We show that there exists a
finite solvable group G, of order prime to p, and a Galois étale cover Y → X,
with Galois group G, which is not ordinary.
On the Density of Elliptic Curves
Wiley - Tập 127 - Trang 23-54 - 2001
We show that 17.9% of all elliptic curves over Q, ordered by their exponential
height, are semistable, and that there is a positive density subset of elliptic
curves for which the root numbers are uniformly distributed. Moreover, for any α
> 1/6 (resp. α > 1/12) the set of Frey curves (resp. all elliptic curves) for
which the generalized Szpiro Conjecture |Δ(E)| ≪α N E 12α is false has density
zer...
On a Jacobian Identity Associated with Real Hyperplane Arrangements
Wiley - Tập 121 - Trang 263-295 - 2000
For $$x \in (a_{j - 1} ,a_j )(j = ,...,p + 1;a_0 : = - \infty ,a_{p + 1} : =
\infty )$$ the mapping $$T_j :w = x - \sum {_{l = 1}^p {\lambda }_l /(x - a_l
)({\lambda }_l >0,a_l } \in {R)}$$ is onto R. It was shown by G. Boole in the
1850's that $$\sum {_{j = 1}^{p + 1} } [(\partial w/\partial x)^{ - 1} ]_{x =
T_j^{ - 1} (w)} = 1$$ We give an n-dimensional analogue of this result. The
proof makes u...
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