The discriminant and the determinant of a hypersurface of even dimension
arXiv:1110.1717 · doi:10.1016/j.cplett.2012.05.046
Abstract
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.
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