We prove new height inequalities for determinantal ideals in a regular local ring, or more generally in a local ring of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns. Introduction. Let φ be a map of vector bundles on a variety X. A wellknown theorem of Eagon and Northcott [EN] gives an upper bound for the codimension of the locus where φ has rank ≤ s...

We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior shifting. We define exterior annihilator numbers analogously to the annihilator nu...

Introduction. In this paper we give a sufficient condition that an algebra have a minimal left (or right) ideal. Specifically, we prove that if A is a complex semisimple Banach algebra with the property that the spectrum of every element in A is at most countable, then A has a minimal left ideal. If A is an ^4*-algebra, we prove that A has a minimal left ideal if the spectrum of every self-adjo...

The LOMOPLAN (LOcal MOnoPLane ANnihilator) lter in three dimensions is a deconvolution lter that takes a volume in and produces two volumes out. The x-output volume results from a rst order prediction-error lter on the x-axis, and the y-output volume is likewise on the y-axis. Synthetic data studies are promising.

We prove that the separating subspace for a derivation on a nonassociative //'-algebra is contained in the annihilator of the algebra. In particular, derivations on nonassociative H* -algebras with zero annihilator are continuous.

The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of Gbundles on a complex compact curve. This result plays a crucial role in the Geometric Langlands program, see [BD], since it insures that the D-modules on the moduli space of G-bundl...

In the classical theory of diophantine approximation, as encountered in the work of Thue, Siegel, Dyson, Roth, and Schmidt, finiteness results are obtained by constructing an auxilliary polynomial. One knows a priori that the polynomial vanishes to high order at certain approximating points and this contradicts an upper bound on the order of vanishing obtained by other techniques. The difficult...

Consider a smooth, geometrically irreducible, projective curve of genus $g\ge 2$ defined over number field degree $d \ge 1$. It has at most finitely many rational points by the Mordell Conjecture, theorem Faltings. We show that is bounded only in terms $g$, $d$ and Mordell–Weil rank curve's Jacobian, thereby answering affirmative question Mazur. In addition we obtain uniform bounds, $g$ $d$, fo...