Witt rings of quadratically presentable fields

Gładki, Paweł; Worytkiewicz, Krzysztof

doi:10.48550/arxiv.1705.04659

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“…For more details, we refer the readers to [Lam05]. It would be interesting to investigate these perspectives in terms of geometry of S following the ideas in [Mar06], [GM12], and [GW17]. Remark 6.…”

Section: Examplementioning

confidence: 99%

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Geometry of hyperfields

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2017

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Given a scheme X over Z and a hyperfield H which is equipped with topology, we endow the set X(H) of H-rational points with a natural topology. We then prove that; (1) when H is the Krasner hyperfield, X(H) is homeomorphic to the underlying space of X, (2) when H is the tropical hyperfield and X is of finite type over a complete non-Archimedean valued field k, X(H) is homeomorphic to the underlying space of the Berkovich analytificaiton X an of X, and (3) when H is the hyperfield of signs, X(H) is homeomorphic to the underlying space of the real scheme X r associated with X.

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Section: Examplementioning

confidence: 99%

“…O. Viro observes that hyperstructures provide a natural algebraic foundation for tropical geometry [Vir10]. M. Marshall, P. Gładki, and K. Worytkiewicz show that hyperstructures simplify (or generalize) certain aspects of quadratic form theory and real algebraic geometry [Mar06], [GM12], [GW17].…”

Section: Introductionmentioning

confidence: 99%

Geometry of hyperfields

Jun

2017

Preprint

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Witt rings of quadratically presentable fields

Cited by 1 publication

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Geometry of hyperfields

Geometry of hyperfields

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