What question did this study set out to answer?

The aim is to demonstrate the fully faithful nature of the functor from nilpotent p-adic spaces to E-infinity coalgebras.

March 25, 2026Open Access

E_ -coalgebras and p-adic homotopy theory

Key Points

The aim is to demonstrate the fully faithful nature of the functor from nilpotent p-adic spaces to E-infinity coalgebras.
Develop a functor from nilpotent p-adic spaces to E-infinity coalgebras over a separably closed field.
Analyze the essential image of simply connected spaces in the context of the coalgebras.
Utilize duality and remove finiteness assumptions from existing theorems.
Confirmed that the functor is fully faithful for separably closed fields of characteristic p > 0.
Identified the essential image of simply connected spaces within the coalgebras framework.
Provided a refinement to Mandell's theorem by addressing finiteness constraints.

Abstract

Abstract We show that for any separably closed field k of characteristic p>0 p > 0, the canonical functor from nilpotent p -adic spaces to E_ E ∞ -coalgebras over k (given by singular chains with coefficients in k) is fully faithful. We also identify the essential image of simply connected spaces inside coalgebras. This dualizes and removes finiteness assumptions from a theorem of Mandell.

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