Skip to content
DraconiticResearch
Search Sources API
186,546 studies31 sourcesUpdated 32 min ago
PreprintCC BY 4.0arXiv

Parahoric motivic Hecke categories in equal and mixed characteristic

  • Sebastian Bartling
  • Rızacan Çiloğlu
Open at sourcePDFDOICite

Abstract

We study constructible ℤ[1/p]-linear étale motives on parahoric Hecke stacks associated with quasi-split tamely ramified reductive groups. We prove a canonical equivalence between their equal-characteristic and Witt-vector incarnations that is monoidal with respect to convolution. This extends Bando's comparison, which concerns split reductive groups and constructible étale sheaves. The proof combines the study of a family of affine Grassmannians for Pappas--Zhu group schemes with the use of the motivic nearby cycles functor.

Related

  1. Characteristic Functions of Parahoric Character Sheaves
    Zhihang Yu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Schematic Functorialities of Birational Motivic Homotopy Categories
    Dipankar Maity
    HALPreprintLicence not statedAlgebra & number theoryGeometry & topologyHAL
  3. On the internal homotopy theory of motivic categories
    Dipankar Maity
    HALPreprintLicence not statedAlgebra & number theoryGeometry & topologyHAL
  4. Motivic Eilenberg--Mac Lane spaces at the characteristic
    Tom Bachmann, Michael J. Hopkins
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  5. Some remarks on realizations defining diagrammatic Hecke categories
    Amit Hazi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{bartling2026parahoric,
  title = {{Parahoric motivic Hecke categories in equal and mixed characteristic}},
  author = {Sebastian Bartling and Rızacan Çiloğlu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05123},
  eprint = {2609.05123},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05123},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Parahoric motivic Hecke categories in equal and mixed characteristic
AU  - Sebastian Bartling
AU  - Rızacan Çiloğlu
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05123
UR  - https://arxiv.org/abs/2609.05123
AB  - We study constructible ℤ[1/p]-linear étale motives on parahoric Hecke stacks associated with quasi-split tamely ramified reductive groups. We prove a canonical equivalence between their equal-characteristic and Witt-vector incarnations that is monoidal with respect to convolution. This extends Bando's comparison, which concerns split reductive groups and constructible étale sheaves. The proof combines the study of a family of affine Grassmannians for Pappas--Zhu group schemes with the use of the motivic nearby cycles functor.
ER  -