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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