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Pré-Publication, Document De Travail Année : 2020

The Space of Valuation Fans and Admissible P-Structures

Résumé

In the whole paper K will be a formally real field, which means that −1 is not a finite sum of squares of elements of K, hence K has characteristic 0. As often in the literature, we shall write real field instead of formally real field. It is well known from Artin-Schreier theory that such fields are exactly those admitting at least one total order compatible with the field structure. After some background in Real Algebra on orderings and valuations, we recall the notions of fans and valuation fans. Thereafter, we introduce and study the space of valuation fans and its relations with the real spectrum of the real holomorphy ring. Finally we provide some steps towards an abstract theory of the space of valuation fans and revisit Marshal's problem of realizability of abstract spaces of orderings.
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hal-03999611 , version 1 (21-02-2023)

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  • HAL Id : hal-03999611 , version 1

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Danielle Gondard-Cozette. The Space of Valuation Fans and Admissible P-Structures. 2023. ⟨hal-03999611⟩
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