Differential forms on arithmetic jet spaces
James Borger, Alexandru Buium
TL;DR
This paper investigates derivations and differential forms on arithmetic jet spaces of smooth schemes across multiple primes, offering new insights into arithmetic Laplacians and de Rham cohomology in this context.
Contribution
It provides a novel interpretation of arithmetic Laplacians and explores the de Rham cohomology of arithmetic jet spaces, advancing understanding in arithmetic geometry.
Findings
New interpretation of arithmetic Laplacians
Analysis of de Rham cohomology of jet spaces
Insights into differential forms on arithmetic schemes
Abstract
We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some specific arithmetic jet spaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry