P-jets of finite algebras. II: $p$-typical Witt rings

Abstract

We study the structure of the $p$-jet spaces of the $p$-typical Witt rings of the $p$-adics. We also study the $p$-jets of the comonad map. These data can be viewed as an arithmetic analogue, for the ring $\mathbb{Z}$, of the Lie groupoid of the line and hence as an infinitesimal version of the Galois group of $\mathbb{Q}$ over “${\mathbb{F}}_1$”.