Entireness ofL-Functions ofϕ-Sheaves on Affine Complete Intersections

Footprint functions of complete intersections

We study the minimum distance function of a complete intersection graded ideal in a polynomial ring with coefficients in a field. For graded ideals of dimension one, whose initial ideal is a complete intersection, we use the footprint function to give a sharp lower bound for the minimum distance function. Then we show some applications to coding theory.

Poles of Zeta Functions of Complete Intersections

A vanishing theorem is proved for`-adic cohomology with compact support on a singular aane complete intersection. As an application, it is shown that for an aane complete intersection deened over a nite eld of q elements, the reciprocal \poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibility of the poles o...

Complete Intersections on General Hypersurfaces

We ask when certain complete intersections of codimension r can lie on a generic hypersurface in Pn. We give a complete answer to this question when 2r ≤ n + 2 in terms of the degrees of the hypersurfaces and of the degrees of the generators of the complete intersection.

On the Regularity of Products and Intersections of Complete Intersections

This paper proves the formulae reg(IJ) ≤ reg(I) + reg(J), reg(I ∩ J) ≤ reg(I) + reg(J) for arbitrary monomial complete intersections I and J , and provides examples showing that these inequalities do not hold for general complete intersections.

Parabolic Sheaves on Surfaces and Affine Lie Algebra Gl N