Geometric and analytic structures on the higher adèles

Oliver Braunling; Michael Groechenig; Jesse Wolfson

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arXiv · 1510.05597

Geometric and analytic structures on the higher adèles

Oliver Braunling·Michael Groechenig·Jesse Wolfson

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Abstract

The adèles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies on a higher local field and no canonical way to pick one. Using the datum of a topology, one can isolate a special class of continuous endomorphisms. Quite differently, one can bypass topology entirely and single out special endomorphisms (global Beilinson-Tate operators) from the geometry of the scheme. Yekutieli's "Conjecture 0.12" proposes that these two notions agree. We prove this.

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BibTeX RIS

Oliver Braunling, Michael Groechenig, Jesse Wolfson. 2017-10-09. Geometric and analytic structures on the higher adèles. https://arxiv.org/abs/1510.05597

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