Quillen stratification in equivariant homotopy theory
We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group , generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as coefficients, and secondly, we categorify it to a result about...
| Autores: | , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:324879 |
| Acesso em linha: | https://ddd.uab.cat/record/324879 https://dx.doi.org/urn:doi:10.1007/s00222-024-01301-0 |
| Access Level: | acceso abierto |
| Palavra-chave: | Algebraic Geometry Algebraic Topology Category Theory, Homological Algebra Commutative Rings and Algebras K-Theory Group Theory and Generalizations |
| Resumo: | We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group , generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as coefficients, and secondly, we categorify it to a result about equivariant modules. Our general stratification theorem is formulated in the language of equivariant tensor-triangular geometry, which we show to be tightly controlled by the non-equivariant tensor-triangular geometry of the geometric fixed points. We then apply our methods to the case of Borel-equivariant Lubin-Tate -theory , for any finite height and any finite group , where we obtain a sharper theorem in the form of cohomological stratification. In particular, this provides a computation of the Balmer spectrum as well as a cohomological parametrization of all localizing ⊗-ideals of the category of equivariant modules over , thereby establishing a finite height analogue of the work of Benson, Iyengar, and Krause in modular representation theory. |
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