Mathematical Research Letters

Volume 25 (2018)

Number 1

The determinant and the discriminant of a complete intersection of even dimension

Pages: 255 – 280

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n1.a11

Author

Yasuhiro Terakado (Graduate School of Mathematical Sciences, University of Tokyo, Japan)

Abstract

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.

Full Text (PDF format)

Received 7 January 2016