Witt vectors and truncation posets

TL;DR

This paper generalizes the concept of Witt vectors by introducing truncation posets, and demonstrates how various structure maps can be encoded through maps of these posets, broadening the theoretical framework.

Contribution

The paper extends Witt vectors to truncation posets and shows how to encode key structure maps using maps between these posets, providing a new conceptual framework.

Findings

Unified encoding of Witt vector operations

Generalization from natural numbers to posets

Framework for future algebraic structures

Abstract

One way to define Witt vectors starts with a truncation poset $S \subset \mathbb{N}$. We generalize Witt vectors to truncation posets, and show how three types of maps of truncation posets can be used to encode the following six structure maps on Witt vectors: addition, multiplication, restriction, Frobenius, Verschiebung and norm.