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Homotopy Spectra and Diophantine Equations

Manin, Yuri I. and Marcolli, Matilde (2021) Homotopy Spectra and Diophantine Equations. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:To Xenia and Paolo, from Yuri and Matilde, with all our love and gratitude. M. Marcolli acknowledges support from NSF grants DMS–1707882 and DMS–2104330 and from NSERC grants RGPIN–2018–04937 and RGPAS–2018–522593. Yu. Manin acknowledges the excellent scientific environment of the Max Planck Institute for Mathematics in Bonn and permanent support of its administration and of the Max Planck Society. We thank the three anonymous referees for a very careful reading of the paper and for providing many detailed comments and suggestions that greatly improved the paper.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Max Planck Institute for MathematicsUNSPECIFIED
Subject Keywords:Algebraic Geometry (math.AG); Number Theory (math.NT); Topology (math.AT)
Classification Code:MSC-classes: 16E35, 11G50, 14G40, 55P43, 16E20, 18F30
Record Number:CaltechAUTHORS:20210825-184614782
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110552
Deposited By: George Porter
Deposited On:25 Aug 2021 22:07
Last Modified:25 Aug 2021 22:07

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