The Theory of Witt Vectors

Abstract

This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (its lambda-algebra structure), the relation to strict p-rings, and an account of the Artin-Hasse exponential.

28 pages. Written in 2007 and posted unmodified to the arXiv by request

Cited by in corpus (9)

• An application of the almost purity theorem to the homological conjectures
• The Relative Canonical Ideal of the Artin-Schreier-Kummer-Witt family of curves
• On the arithmetic of Z_p-extensions
• An embedding problem of Noetherian rings into the Witt vectors
• On p-adic Frobenius lifts and p-adic periods, from a Deformation Theory viewpoint
• Maximal Cohen-Macaulay modules over local toric rings
• Localizations of Morava E-theory and deformations of formal groups
• Witt vector rings and quotients of monoid algebras
• Genus growth in ${\mathbb{Z}}_p$-towers of function fields