Mathematical Research Letters
Volume 25 (2018)
The determinant and the discriminant of a complete intersection of even dimension
Pages: 255 – 280
The determinant of the Galois action on the $\ell$-adic cohomology of the middle degree of a proper smooth variety of even dimension defines a quadratic character of the absolute Galois group of the base field. In this article, we show that for a complete intersection of even dimension in a projective space, the character is computed via the square root of the discriminant of the defining polynomials of the variety.
Received 7 January 2016