Some observations on Karoubian complete strongly exceptional posets on the projective homogeneous varieties

2009/11/13 by Masaharu Kaneda, Kaneda, Masaharu, Jiachen Ye +1 · 1 citation
Mathematics · #20G05 14B10 14F05 14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14B10 #msc:14F05 #msc:14M15 #msc:20G05

paper · pdf · doi:10.48550/arxiv.0911.2568

20 pagies, this is a consise version

openalex publication_date 2009/11/13 · arxiv created 2009/12/23 · arxiv updated 2010/01/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let \cP=G/P be a homogeneous projective variety with G a reductive group and P a parabolic subgroup. In positive characteristic we exhibit for G of low rank a Karoubian complete strongly exceptional poset of locally free sheaves appearing in the Frobenius direct image of the structure sheaf of G/P. These sheaves are all defined over \bbZ, so by base change provide a Karoubian complete strongly exceptional poset on \cP over \bbC, adding to the list of classical results by Beilinson and Kapranov on the Grassmannians and the quadrics over \bbC.

Citations

• Tilting bundles via the Frobenius morphism

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• The Frobenius morphism on flag varieties, II

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