Harmonic analysis and the Riemann-Roch theorem
D. V. Osipov, A. N. Parshin
TL;DR
This paper extends harmonic analysis and adelic theory to derive the Riemann-Roch theorem for algebraic surfaces over finite fields, building on previous work with two-dimensional Poisson formulas.
Contribution
It introduces a new proof of the Riemann-Roch theorem for surfaces using adelic and harmonic analysis methods, advancing the theoretical framework.
Findings
Derived the Riemann-Roch formula for algebraic surfaces over finite fields
Connected two-dimensional Poisson formulas with adelic theory
Extended previous mathematical frameworks to higher dimensions
Abstract
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theory we obtain the Riemann-Roch formula on a projective smooth algebraic surface over a finite field.
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