Let $K$ be a perfect field with characteristic $>0$ and $\mathcal{H}$ the category of graded connected abelian hopf algebras over $K$.
By a theorem of Schoeller there is a canonical equivalence between $\mathcal{H}$ and the category of
Dieudonne modules over $K.$

Is there a homotopy-coherent version of Dieudonne modules and a homotopy-coherent version of Schoeller's theorem that identifies a derived version of Dieudonne module with a connected $E_\infty$-hopf algebra over $K$?

By definition an $E_\infty$-hopf algebra over $K$ is an abelian group object (in the derived sense) in the $\infty$-category of $E_\infty$-coalgebras in the derived $\infty$-category of $K,$ which is connected if its homology is canonically $K.$