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- W3120673674 abstract "The classical version of B'ezout's Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using work of Kass and Wickelgren, we prove a version of B'ezout's Theorem over any perfect field by giving a bilinear form-valued count of the intersection points of hypersurfaces in projective space. Over non-algebraically closed fields, this enriched B'ezout's Theorem imposes a relation on the gradients of the hypersurfaces at their intersection points. As corollaries, we obtain arithmetic-geometric versions of B'ezout's Theorem over the reals, rationals, and finite fields of odd characteristic." @default.
- W3120673674 created "2021-01-18" @default.
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- W3120673674 date "2021-01-09" @default.
- W3120673674 modified "2023-10-17" @default.
- W3120673674 title "An arithmetic enrichment of Bézout’s Theorem" @default.
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- W3120673674 doi "https://doi.org/10.1007/s00208-020-02120-3" @default.
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