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Motivic modular forms from equivariant stable homotopy theory

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arxiv 1704.04547 v2 pith:XB5M4DHD submitted 2017-04-14 math.AT

Nicolas Ricka This is my paper · ORCID
classification math.AT
keywords motivicspectrumequivariantformsmachinerymodularproducealgebra
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abstract

In this paper, we produce a cellular motivic spectrum of motivic modular forms over $\R$ and $\C$, answering positively to a conjecture of Dan Isaksen. This spectrum is constructed to have the appropriate cohomology, as a module over the relevant motivic Steenrod algebra. We first produce a $\G$-equivariant version of this spectrum, and then use a machinery to construct a motivic spectrum from an equivariant one. We believe that this machinery will be of independent interest.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. C_2-equivariant stable homotopy from real motivic stable homotopy

    math.AT 2019-08 accept novelty 7.0 of 10

    Betti realization identifies the p-complete C2-equivariant stable homotopy category as a localization of the p-complete cellular real motivic stable homotopy category, yielding computable RO(C2)-graded homotopy groups...

  2. Conjugation Spaces are Cohomologically Pure

    math.AT 2019-08 accept novelty 7.0 of 10

    For finite-type spaces with a C2-action, having a conjugation frame is equivalent to being homologically pure, meaning X ∧ HF splits as a wedge of sign-representation suspensions of HF.

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