Cartier's first theorem for Witt vectors on Z_{>= 0}^n - 0

TL;DR

This paper extends Cartier's first theorem to Witt vectors on Z_{>= 0}^n - 0, showing their duality properties and representing certain functors for formal groups.

Contribution

It generalizes Cartier's theorem to higher dimensions and establishes duality and representability results for Witt vectors on Z_{>= 0}^n - 0.

Findings

Witt vectors represent the functor mapping formal schemes to formal groups.

Witt vectors are self-dual over Q-algebras or when n=1.

Extension of Cartier's theorem to multi-dimensional cases.

Abstract

We show that the dual of the Witt vectors on Z_{\geq 0}^n - 0 as defined by Angeltveit, Gerhardt, Hill, and Lindenstrauss represent the functor taking a commutative formal group G to the maps of formal schemes Ahat^n -> G, and that the Witt vectors are self-dual for Q-algebras or when n=1.