Brian Edward Crawley

On Crawley Modules *

This continues recent work in a paper by Corner, Göbel and Goldsmith [2]. A particular question was left open: Is it possible to carry over the results concerning the undecidability of torsion–free Crawley groups to modules over the ring of p-adic integers? We will confirm this and also strengthen one of the results in [2] by replacing the hypothesis of ♦ by CH. For details see the introduction.

Edward.

Polarizations Brian

If A is an abelian variety over a field, then to give a projective embedding of A is more or less to give an ample line bundle on A. Over C, such data can be expressed in terms of a positive-definite Riemann form on the homology lattice. Hence, we consider ample line bundles on general abelian varieties to be a “positivity” structure. In a sense that will be explained, just as we view abelian v...

2 Brian

In this paper the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category OS for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L “looks like” the cohomology with coefficients in a finite-dimensional module, as in Kostant’s theorem. A complete classification of these “Kostant modules”...

Brian Zuckerman