Homotopy Spectra and Diophantine Equations
arXiv:2101.00197
Abstract
Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, - topology and number theory, - was built only during the last fifty years. This bridge is the theory of spectra in stable homotopy theory. This connection poses the challenge: discover new information in number theory using the independently-developed machinery of homotopy theory. In this combined research/survey paper we suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.
arXiv comment87 pages amstex
References in corpus (14)
- The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
- The Grothendieck group of algebraic stacks
- Integral points of bounded height on partial equivariant compactifications of vector groups
- Zeta functions, Grothendieck groups, and the Witt ring
- Produit eulérien motivique et courbes rationnelles sur les variétés toriques
- Very strong approximation for certain algebraic varieties
- Motivic height zeta functions
- Beyond heights: slopes and distribution of rational points
- Motivic Poisson summation
- Exponentiation of motivic measures
- Brauer and Etale Homotopy Obstructions to Rational Points on Open Covers
- On upper bounds of Manin type
- The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
- Rational homotopy type and computability