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| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2011年07月27日(水)
16:00-18:15 数理科学研究科棟(駒場) 123号室
いつもと時間,教室が異なりますのでご注意下さい.
斎藤毅 氏 (東京大学数理科学研究科) 16:00-17:00
Discriminants and determinant of a hypersurface of even dimension (ENGLISH)
Multiplicities of discriminants (ENGLISH)
いつもと時間,教室が異なりますのでご注意下さい.
斎藤毅 氏 (東京大学数理科学研究科) 16:00-17:00
Discriminants and determinant of a hypersurface of even dimension (ENGLISH)
[ 講演概要 ]
The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
defining polynomial. We determine the sign involved by testing
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Dennis Eriksson 氏 (University of Gothenburg) 17:15-18:15The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
defining polynomial. We determine the sign involved by testing
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Multiplicities of discriminants (ENGLISH)
[ 講演概要 ]
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.
