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2011 The basic geometry of Witt vectors, I The affine case
James Borger
Algebra Number Theory 5(2): 231-285 (2011). DOI: 10.2140/ant.2011.5.231


We give a concrete description of the category of étale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical p-typical and big Witt vector functors but also for certain analogues over arbitrary local and global fields. The basic theory of these generalized Witt vectors is developed from the point of view of commuting Frobenius lifts and their universal properties, which is a new approach even for classical Witt vectors. Our larger purpose is to provide the affine foundations for the algebraic geometry of generalized Witt schemes and arithmetic jet spaces, so the basics are developed in some detail, with an eye toward future applications.


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James Borger. "The basic geometry of Witt vectors, I The affine case." Algebra Number Theory 5 (2) 231 - 285, 2011.


Received: 13 May 2010; Revised: 8 August 2010; Accepted: 13 October 2010; Published: 2011
First available in Project Euclid: 21 December 2017

zbMATH: 1276.13018
MathSciNet: MR2833791
Digital Object Identifier: 10.2140/ant.2011.5.231

Primary: 13F35

Keywords: Frobenius lift , lambda-ring , plethory , Witt space , Witt vector

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2011
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