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


Yasuhiro Terakado ( Academia Sinica )
16:00 - 16:50
Room 101, Mathematics Research Center Building (ori. New Math. Bldg.)

The determinant of the Galois action on the l-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 talk, 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.