Abstract

The etale cohomology group of a proper smooth variety has a natural action of the absolute Galois group of the base field. This enables us to investigate the arithmetic of the variety.

In this talk, we show that for a smooth complete intersection of even dimension, the quadratic character of the absolute Galois group defined by the determinant of the etale cohomology is computed via the square root of the discriminant of defining polynomials of the variety.