Krull-tropical hypersurfaces

Details Krull-tropical hypersurfaces Krull-tropical hypersurfaces

2009-03-31

arxiv.org/abs/0903.5375v2

Mathematics

Algebraic Geometry

12 pages

Scientific paper

The concepts of tropical-semiring and tropical hypersurface, are extended for an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator "tropicalization" we conclude with an extension of Kapranov's theorem to algebraically closed fields together with a valuation over an ordered group.

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