Affine combinations in affine schemes
Anders Kock
TL;DR
This paper proves that finite sets of mutually neighboring points in an affine scheme can be combined affine-wise, with the combination preserving neighbor relations under any map, revealing new structural properties of affine schemes.
Contribution
It introduces the concept that finite neighbor point sets in affine schemes admit affine combinations that are preserved by all maps, expanding understanding of affine scheme structure.
Findings
Finite neighbor point sets admit affine combinations.
Affine combinations are preserved by any scheme map.
The combined point remains neighbor to all original points.
Abstract
We prove that finite sets of mutual neighbor points in an affine scheme admit affine combinations, preserved by any map. Furthermore, such combination has a value which is neighbor point of all the original points.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons