On $p$-adic interpolation of motivic Eisenstein classes

TL;DR

This paper demonstrates that motivic Eisenstein classes linked to polylogarithms of commutative group schemes can be interpolated in p-adic étale cohomology, extending previous elliptic curve results and enabling easier handling of degeneration issues.

Contribution

It introduces a p-adic interpolation framework for motivic Eisenstein classes of commutative group schemes, broadening applicability beyond elliptic curves.

Findings

Successful p-adic interpolation of motivic Eisenstein classes

Enhanced flexibility for one-dimensional commutative groups

Facilitates analysis of degeneration phenomena

Abstract

In this paper we prove that the motivic Eisenstein classes associated to polylogarithms of commutative group schemes can be $p$-adically interpolated in \'etale cohomology. This generalizes results for elliptic curves obtained in our former work. Already for one dimensional commutative groups the results proved here are much more flexible as they allow to treat degeneration questions easily.