Mathematical Research Letters

Volume 19 (2012)

Number 4

The discriminant and the determinant of a hypersurface of even dimension

Pages: 855 – 871

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n4.a10

Author

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

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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