Cohomology of Line Bundles on the Flag Variety for Type G_2
Henning Haahr Andersen, Masaharu Kaneda

TL;DR
This paper investigates the cohomology of line bundles on the flag variety for the algebraic group of type G_2 over fields of positive characteristic and quantum groups at roots of unity, providing complete vanishing criteria.
Contribution
It provides a full characterization of the vanishing behavior of cohomology modules for line bundles induced by characters from the lowest p^2-alcoves in characteristic p>0 and for quantum groups at roots of unity.
Findings
Complete determination of cohomology vanishing in characteristic p>0.
Full description of quantum cohomology vanishing at roots of unity.
Results applicable to all characters in the specified alcoves.
Abstract
In the case of an almost simple algebraic group of type over a field of characteristic we study the cohomology modules of line bundles on the flag variety for . Our main result is a complete determination of the vanishing behavior of such cohomology in the case where the line bundles in question are induced by characters from the lowest -alcoves. When is the quantum group corresponding to whose parameter is a complex root of unity of order prime to 6 we give a complete (i.e. covering all characters) description of the vanishing behavior for the corresponding quantized cohomology modules.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory
