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We study the subgroup B0(G) of H2(G,Q/Z) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of lie type Ae. [ABSTRACT FROM AUTHOR]

We study the subgroup B0(G) of H²(G, &doubleQ;/&doubleZ;) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of Lie type Aℓ. [ABSTRACT FROM AUTHOR]

We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich's little Picard theorem, which says there are no nonconstant rigid analytic maps from the affine line to nonsingular projective curves of positive genus, and of Cherry's result that there are no nonconstant rigid analytic maps from the affine line to Abelian varieties. Furthermore, we use the lemma to prove new theorems of little and big Picard type for dominant mappings, in close analogy with Griffiths and King. For the little Picard type theorem, we prove that if X is a smooth projective variety with a simple normal crossings divisor D such that (X, D) has nonnegative logarithmic Kodaira dimension, then there are no dominant rigid analytic maps f from Am to X \ D. For the big Picard type theorem, we prove that if Y is a nonsingular rigid analytic space, E is an effective simple normal crossings divisor on Y, and if X is a smooth projective variety with a simple normal crossings divisor D such that (X, D) is of log-general type, then any dominant rigid analytic map f: Y \ E → X \ D extends to an analytic map from Y to X. [ABSTRACT FROM AUTHOR]

We study the subgroup B0(G) of H2(G,Q/Z) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of lie type Ae. [ABSTRACT FROM AUTHOR]