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PreprintarXiv licencearXiv

Verdier-Type Category, Geometric Serre's conditions and perversity

  • Shang Xu
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Abstract

We generalize Serre's conditions for coherent sheaves to triangulated categories equipped with a t-structure and duality, which we call Verdier-type categories. We present examples of such categories and their associated Serre conditions, then focus on constructible sheaves, where we refer to these conditions as geometric Serre conditions. We investigate their relationship with perversity and illustrate the theory through a range of examples. Finally, we prove a geometric version of the Auslander-Reiten conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026verdiertype,
  title = {{Verdier-Type Category, Geometric Serre's conditions and perversity}},
  author = {Shang Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01146},
  eprint = {2610.01146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01146},
}
RIS
TY  - UNPB
TI  - Verdier-Type Category, Geometric Serre's conditions and perversity
AU  - Shang Xu
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.01146
UR  - https://arxiv.org/abs/2610.01146
AB  - We generalize Serre's conditions for coherent sheaves to triangulated categories equipped with a t-structure and duality, which we call Verdier-type categories. We present examples of such categories and their associated Serre conditions, then focus on constructible sheaves, where we refer to these conditions as geometric Serre conditions. We investigate their relationship with perversity and illustrate the theory through a range of examples. Finally, we prove a geometric version of the Auslander-Reiten conjecture.
ER  -