Mathematical Research Letters
Volume 19 (2012)
The discriminant and the determinant of a hypersurface of even dimension
Pages: 855 – 871
For a smooth hypersurface of even dimension, the quadratic character of the absolute Galois group defined by the determinant of the ℓ-adic cohomology of middle dimension is computed via the square root of the discriminant of a defining polynomial of the hypersurface.