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- W2914446055 abstract "This paper lays out a foundation for a theory of supertropical algebraic geometry, relying on commutative $nu$-algebra. To this end, the paper introduces $mathfrak{q}$-congruences, carried over $nu$-semirings, whose distinguished ghost and tangible clusters allow both quotienting and localization. Utilizing these clusters, $mathfrak{g}$-prime, $mathfrak{g}$-radical, and maximal $mathfrak{q}$-congruences are naturally defined, satisfying the classical relations among analogous ideals. Thus, a foundation of systematic theory of commutative $nu$-algebra is laid. In this framework, the underlying spaces for a theoretic construction of schemes are spectra of $mathfrak{g}$-prime congruences, over which the correspondences between $mathfrak{q}$-congruences and varieties emerge directly. Thereby, scheme theory within supertropical algebraic geometry follows the Grothendieck approach, and is applicable to polyhedral geometry." @default.
- W2914446055 created "2019-02-21" @default.
- W2914446055 creator A5020188998 @default.
- W2914446055 date "2019-01-23" @default.
- W2914446055 modified "2023-09-25" @default.
- W2914446055 title "Commutative ν-Algebra and Supertropical Algebraic Geometry" @default.
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