Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Frobenius morphism on flag varieties, I   In this paper, given a semisimple algebraic group $\bf G$ of rank 2, we
construct a special semiorthogonal decomposition in the derived category of
coherent sheaves on the flag variety ${\bf G}/{\bf B}$. These decompositions
are defined over the localization ${\mathbb Z}_{\rm S}$, where $\rm S$ is the
set of bad primes for $\bf G$, while their block structure is compatible with
the Bruhat order on Schubert varieties. The non-standard $t$-structures on
${\rm D}^b({\bf G}/{\bf B})$ defined by these decompositions are self-dual with
respect to the duality ${\mathcal RHom}_{{\bf G}/{\bf B}}(-,\omega _{{\bf
G}/{\bf B}}^{\frac{1}{2}})$ given by the square root of the canonical sheaf of
${\bf G}/{\bf B}$. For the groups of classical type, this allows to construct
an explicit decomposition of the higher Frobenii pushforward bundles ${\sf
F}^n_{\ast}{\mathcal O}_{{\bf G}/{\bf B}}$ into a direct sum of indecomposable
bundles. When $p>h$, the Coxeer number of the corresponding group, this set of
indecomposable bundles forms a full exceptional collection in ${\rm D}^b({\bf
G}/{\bf B})$ defined over ${\mathbb Z}_{\rm S}$.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg