A deformation of Borel equivariant homotopy

Gabriel Angelini-Knoll; Mark Behrens; Eva Belmont; Hana Jia Kong

A deformation of Borel equivariant homotopy

Algebraic Topology 2025-11-18 v3

Authors: Gabriel Angelini-Knoll , Mark Behrens , Eva Belmont , Hana Jia Kong

Abstract

We describe a deformation of the $\infty$ -category of Borel $G$ -spectra for a finite group $G$ . This provides a new presentation of the $a$ -complete real Artin--Tate motivic stable homotopy category when $G=C_2$ and gives a new interpretation of the $a$ -completed $C_2$ -effective slice spectral sequence. As a new computational tool, we present a modified Adams--Novikov spectral sequence which computes the $RO(G)$ -graded Mackey functor valued homotopy of Borel $G$ -spectra.

Keywords

borel equivariant homotopy infinity-category g-spectra motivic stable homotopy adams-novikov spectral sequence mackey functor

Cite

@article{arxiv.2308.01873,
  title  = {A deformation of Borel equivariant homotopy},
  author = {Gabriel Angelini-Knoll and Mark Behrens and Eva Belmont and Hana Jia Kong},
  journal= {arXiv preprint arXiv:2308.01873},
  year   = {2025}
}

Comments

Revised discussion on convergence and MUR-projective case. Accepted in Advances in Mathematics. 51 pages

A deformation of Borel equivariant homotopy

Abstract

Keywords

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