Kernel of Arithmetic Jet Spaces
Arnab Saha

TL;DR
This paper develops a theory of arithmetic jet spaces and Witt vectors over Dedekind domains, establishing structural results and applications to formal group schemes and point subgroups, with implications for algebraic geometry and number theory.
Contribution
It introduces $m$-shifted $ ext{π}$-typical Witt vectors and a lift of Frobenius, providing new structural insights into arithmetic jet spaces and formal group schemes.
Findings
$N^{mn} ext{G}$ is isomorphic to $J^{n-1}(N^{m1} ext{G})$ for $ ext{π}$-formal groups.
$J^n ext{G}$ is a canonical extension of $ ext{G}$ by Witt vector schemes.
Characterization of subgroup points $G( ext{π}^{n+1}R)$ in terms of reduction modulo $ ext{π}^{n+1}$.
Abstract
Since the results here have been superseded by another paper cowritten by the author, this article is available for reference purposes only. Fix a Dedekind domain and a non-zero prime in it along with a uniformizer . In the first part of the paper, we construct -shifted -typical Witt vectors for any algebra of length . They are a generalization of the usual -typical Witt vectors. Along with it we construct a lift of Frobenius, called the lateral Frobenius and show that it satisfies a natural identity with the usual Frobenius map. Now given a group scheme defined over , where is an -algebra with a fixed -derivation on it, one naturally considers the -th arithmetic jet space whose points are…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
