Tasos Moulinos - Filtered formal groups, Cartier duality, and derived algebraic geometry

epiga:7640 - Épijournal de Géométrie Algébrique, March 5, 2024, Volume 8 - https://doi.org/10.46298/epiga.2024.7640
Filtered formal groups, Cartier duality, and derived algebraic geometryArticle

Authors: Tasos Moulinos

    We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived algebraic geometry. Applied to the unit section of a formal group $\widehat{\mathbb{G}}$, this provides a $\mathbb{G}_m$-equivariant degeneration of $\widehat{\mathbb{G}}$ to its tangent Lie algebra. We prove a unicity result on complete filtrations, which, in particular, identifies the resulting filtration on the coordinate algebra of this deformation with the adic filtration on the coordinate algebra of $\widehat{\mathbb{G}}$. We use this in a special case, together with the aforementioned notion of Cartier duality, to recover the filtration on the filtered circle of [MRT19]. Finally, we investigate some properties of $\widehat{\mathbb{G}}$-Hochschild homology set out in loc. cit., and describe "lifts" of these invariants to the setting of spectral algebraic geometry.


    Volume: Volume 8
    Published on: March 5, 2024
    Accepted on: October 21, 2023
    Submitted on: July 1, 2021
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Algebraic Topology,Mathematics - K-Theory and Homology
    Funding:
      Source : OpenAIRE Graph
    • New Directions in Derived Algebraic Geometry; Funder: European Commission; Code: 741501

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