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Jean-Pierre Serre 
2009-07-01 
10:30 - 11:30 
101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Let f(x) be a family of polynomials in several variables, with coefficients in the ring of integers. For every prime number p, let N(f;p) be the number of solutions mod p of the system of equations f(x) = 0 mod p. We shall discuss the way N(f;p) varies with p; we shall be especially interested in the relations of N(f;p) with the cohomology of the complex space defined by the equations f(x) = 0.