TL;DR
This paper introduces a numerical method for cohomology that replaces vector spaces and linear maps with real numbers representing their dimensions and ranks, refining existing ideas in Arakelov bundle cohomology.
Contribution
It presents a novel numerical approach to cohomology, simplifying complex algebraic structures into real-valued computations.
Findings
Provides a new framework for cohomology calculations
Refines ideas of Van der Geer and Schoof on Arakelov bundles
Enables numerical analysis of cohomological properties
Abstract
We develop a numerical approach to cohomology. Essentially, vector spaces and linear maps are replaced by real numbers, which represent dimensions of vector spaces and ranks of linear maps. We use this to refine ideas of Van der Geer and Schoof about the cohomology of Arakelov bundles.
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