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An Expository Proof of Bézout's Theorem

John McGee
Organization: Radford University

Wolfram Technology Conference 2014
Conference location

Champaign, Illinois, USA

Bezout's Theorem tells us that the count of the number of intersection points between two algebraic curves h,g in F[x,y] is equal to the product of the degrees of the polynomials defining the curves. In order to make this precise we must seek solutions in the algebraic closure of the field, work in projective space, and account for intersection multiplicity. In this talk we summarize an expository proof of Bezout's Theorem. Our proof is based on an problem set given in Appendix A of Silverman and Tate's textbook: Rational Points on Elliptic Curves. Our contribution fills in the details of the proof and provides concrete examples to illuminate the key ideas. This work was performed as part of an undergraduate research project with student James Grenier.

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BezoutsTheorem_Wolfram_2014_McGee_Final.nb (2.2 MB) - Mathematica Notebook