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Bezout's theorem and nonabelian homological algebra
Jacob Lurie (Harvard University)
September 7, 2005

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Abstract: We will begin with a review of the classical theorem of Bezout, which computes the number of intersection points of two algebraic curves in the projective plane, provided that they meet transversely. In the case of nontransverse intersections, one can make a similar assertion provided that one counts the intersection points with the correct multiplicities. The search for the correct intersection multiplicities will lead us into the world of "nonabelian homological algebra", a theory which is a mixture of classical algebra and homotopy theory.

Lecture Notes (by D. Ben-Zvi): pages 1, 2, 3, 4, 5, 6, 7, 8.

See also the introduction to Lurie's thesis(pdf) in which Bezout's theorem and its nonabelian homological setting are discussed.

 

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