Mathematical Research Letters

Volume 19 (2012)

Number 4

The discriminant and the determinant of a hypersurface of even dimension

Pages: 855 – 871



Takeshi Saito (Department of Mathematical Sciences, University of Tokyo, Japan)


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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