Corpus ID: 212736956

# An arithmetic enrichment of B\'ezout's Theorem

@article{McKean2020AnAE,
title={An arithmetic enrichment of B\'ezout's Theorem},
author={S. McKean},
journal={arXiv: Algebraic Geometry},
year={2020}
}
• S. McKean
• Published 2020
• Mathematics
• arXiv: Algebraic Geometry
• The classical version of Bezout'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 Bezout'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 Bezout's Theorem imposes a relation on the gradients of the hypersurfaces… CONTINUE READING
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