Cohomology Groups of Locally q-Complete Morphisms with r-Complete Base.
q-completeness and q-concavity of the union of open subspaces.
Some convexity properties of morphisms of complex spaces.
Cohomology with compact supports for q-complete spaces.
Invariance of cohomological q-completeness under finite holomorphic surjections.
Holomorphic q-hulls in top degrees.
Approximation theorems and homology of q-Runge domains in complex spaces.
The analyticity of -concave sets of locally finite Hausdorff measure
We prove the analyticity of -concave sets of locally finite Hausdorff -measure in a -dimensional complex space. We apply it to give a removability criterion for meromorphic maps with values in -complete spaces.
Pseudoconvex domains over -complete manifolds
Grauert's line bundle convexity, reduction and Riemann domains
We consider a convexity notion for complex spaces with respect to a holomorphic line bundle over . This definition has been introduced by Grauert and, when is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if separates each point of , then can be realized as a Riemann domain over the complex projective space...
A cohomological Steinness criterion for holomorphically spreadable complex spaces
Let be a complex space of dimension , not necessarily reduced, whose cohomology groups are of finite dimension (as complex vector spaces). We show that is Stein (resp., -convex) if, and only if, is holomorphically spreadable (resp., is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for -convexity.
Integer points unusually close to elliptic curves.
Differences between powers of a primitive root.
Trace functions and Galois invariant p-adic measures.
Cousin-I spaces and domains of holomorphy
We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.
A class of algebraic-exponential congruences modulo .
On the set .
An irreducibility criterion for polynomials in several variables
The Behavior of Rigid Analytic Functions Around Orbits of Elements of <>
The -adic measure on the orbit of an element of
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