Bezout's theorem and nonabelian homological algebra

Jacob Lurie (Harvard University)
September 7, 2005

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.