The Frobenius morphism on flag varieties, I
Alexander Samokhin

TL;DR
This paper constructs special semiorthogonal decompositions for derived categories of flag varieties of rank 2 groups, enabling explicit descriptions of Frobenius pushforward bundles and full exceptional collections in certain cases.
Contribution
It introduces new semiorthogonal decompositions compatible with Bruhat order, over localized integers, and constructs explicit decompositions of Frobenius pushforwards for classical groups.
Findings
Decomposition of Frobenius pushforward bundles into indecomposables.
Construction of self-dual t-structures on derived categories.
Existence of full exceptional collections when p > h.
Abstract
In this paper, given a semisimple algebraic group of rank 2, we construct a special semiorthogonal decomposition in the derived category of coherent sheaves on the flag variety . These decompositions are defined over the localization , where is the set of bad primes for , while their block structure is compatible with the Bruhat order on Schubert varieties. The non-standard -structures on defined by these decompositions are self-dual with respect to the duality given by the square root of the canonical sheaf of . For the groups of classical type, this allows to construct an explicit decomposition of the higher Frobenii pushforward bundles into a direct…
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics
