7,134 research outputs found
Automorphisms of Drinfeld half-spaces over a finite field
We show that the automorphism group of Drinfeld's half-space over a finite
field is the projective linear group of the underlying vector space. The proof
of this result uses analytic geometry in the sense of Berkovich over the finite
field equipped with the trivial valuation. We also take into account extensions
of the base field.Comment: 15 page
Irreducible Modules for Extended Affine Lie Algebras
We construct irreducible modules for twisted toroidal Lie algebras and
extended affine Lie algebras. This is done by combining the representation
theory of untwisted toroidal algebras with the technique of thin coverings of
modules. We illustrate our method with examples of extended affine Lie algebras
of Clifford type.Comment: 37 page
Criteria for the density property of complex manifolds
In this paper we suggest new effective criteria for the density property.
This enables us to give a trivial proof of the original Anders\'en-Lempert
result and to establish (almost free of charge) the algebraic density property
for all linear algebraic groups whose connected components are different from
tori or \C_+. As another application of this approach we tackle the question
(asked among others by F. Forstneri\v{c}) about the density of algebraic vector
fields on Euclidean space vanishing on a codimension 2 subvariety.Comment: to appear in Invent. Mat
Integral point sets over finite fields
We consider point sets in the affine plane where each
Euclidean distance of two points is an element of . These sets
are called integral point sets and were originally defined in -dimensional
Euclidean spaces . We determine their maximal cardinality
. For arbitrary commutative rings
instead of or for further restrictions as no three points on a
line or no four points on a circle we give partial results. Additionally we
study the geometric structure of the examples with maximum cardinality.Comment: 22 pages, 4 figure
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