Weil conjectures 4 Fermat hypersurfaces
Channel: Richard E Borcherds
Date: 20/10/2020

This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. The fact that the absolute value of Gauss sums is the square root of p turns out to imply the Riemann hypothesis for these surfaces.

Weil's paper can be found at https://www.projecteuclid.org/euclid.bams/1183513798