Article Dans Une Revue Épijournal de Géométrie Algébrique Année : 2024

Filtered formal groups, Cartier duality, and derived algebraic geometry

Résumé

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. Comment: Publication version

Dates et versions

hal-04977412 , version 1 (05-03-2025)

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Tasos Moulinos. Filtered formal groups, Cartier duality, and derived algebraic geometry. Épijournal de Géométrie Algébrique, 2024, Volume 8, ⟨10.46298/epiga.2024.7640⟩. ⟨hal-04977412⟩
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