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Semiorthogonal decompositions for families of twisted flag varieties

  • Alexey Ananyevskiy
  • Alexander Samokhin
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Abstract

We show that the derived categories of smooth families of twisted generalized flag varieties admit semiorthogonal decompositions into derived categories of twisted sheaves over the base. In particular, we obtain a categorification of Panin's computation of the Quillen K-theory of twisted flag varieties. The main ingredient is a generalization of the Samokhin-van der Kallen semiorthogonal decomposition for representation categories of parabolic subgroups from split simply connected semisimple groups to arbitrary quasi-split semisimple groups, including non-simply connected cases.

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Cite

BibTeXRIS
BibTeX
@misc{ananyevskiy2026semiorthogonal,
  title = {{Semiorthogonal decompositions for families of twisted flag varieties}},
  author = {Alexey Ananyevskiy and Alexander Samokhin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05203},
  eprint = {2609.05203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05203},
}
RIS
TY  - UNPB
TI  - Semiorthogonal decompositions for families of twisted flag varieties
AU  - Alexey Ananyevskiy
AU  - Alexander Samokhin
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05203
UR  - https://arxiv.org/abs/2609.05203
AB  - We show that the derived categories of smooth families of twisted generalized flag varieties admit semiorthogonal decompositions into derived categories of twisted sheaves over the base. In particular, we obtain a categorification of Panin's computation of the Quillen K-theory of twisted flag varieties. The main ingredient is a generalization of the Samokhin-van der Kallen semiorthogonal decomposition for representation categories of parabolic subgroups from split simply connected semisimple groups to arbitrary quasi-split semisimple groups, including non-simply connected cases.
ER  -