Sekiguchi-Suwa theory revisited

TL;DR

This paper revisits the Sekiguchi-Suwa theory, providing a comprehensive construction of cyclic isogenies unifying Kummer and Artin-Schreier-Witt theories over arbitrary base rings, and extends related results.

Contribution

It offers a complete, generalized construction of the cyclic isogeny unifying key theories over any base ring, enhancing understanding of models of roots of unity.

Findings

Unified construction of cyclic isogenies

Extension of results to arbitrary base rings

Improved models of roots of unity

Abstract

We present an account of the construction by S. Sekiguchi and N. Suwa of a cyclic isogeny of affine smooth group schemes unifying the Kummer and Artin-Schreier-Witt isogenies. We complete the construction over an arbitrary base ring. We extend the statements of some results in a form adapted to a further investigation of the models of the group schemes of roots of unity.