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A fundamental problem at the confluence of algebraic geometry andrepresentation theory is to describe the cohomology of line bundles on flagvarieties over a field of characteristic p. When p=0, the solution is given bythe celebrated Borel-Weil-Bott Theorem, while for p>0 the problem is widelyopen. In this note we describe a collection of open questions that arise fromthe study of particular cases of the general theory, focusing on theircombinatorial and commutative algebra aspects.

Some questions arising from the study of cohomology on flag varieties