The Frobenius morphism on flag varieties, II
Alexander Samokhin

TL;DR
This paper investigates the Frobenius pushforward of the structure sheaf on certain flag varieties, revealing a decomposition into indecomposable bundles and proposing a conjecture for the general case.
Contribution
It explicitly determines the decomposition of the Frobenius pushforward on specific adjoint varieties and formulates a conjecture for broader cases.
Findings
Decomposition into indecomposable bundles is characteristic-independent.
The set forms a strong full exceptional collection in the derived category.
Provides a conjectural framework for the general case.
Abstract
In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius pushforward of the structure sheaf on the adjoint varieties in type and . We show that this pushforward sheaf decomposes into a direct sum of indecomposable bundles and explicitly determine this set that does not depend of the characteristic. In accordance with the results of arXiv:0707.0913, this set forms a strong full exceptional collection in the derived category of coherent sheaves. These computations lead to a natural conjectural answer in the general case that we state at the end.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry
