20/07/15 23:41:30.47 hRRJMwM+.net
>>151 追加
これは、米高校生の数学ソフトによる 計算レポートだが
なかなかレベル高いね
URLﾘﾝｸ(scholarcommons.sc.edu)
The Relationship between Conductor and Discriminant of an Elliptic Curve over Q
Nico Adamo
Heathwood Hall Episcopal School, 9th Grade, Columbia SC
(抜粋)
Saito (1988) establishes a relationship between two invariants associated with a smooth projective curve,
the conductor and discriminant. Saito defined the conductor of an arbitrary scheme
of finite type using p-adic etale cohomology. He used a definition of Deligne for the discriminant
as measuring defects in a canonical isomorphism between powers of relative dualizing sheaf of
smooth projective curves. The researcher in this paper uses the fact that this relationship is
analogous to that of conductor to discriminant in the case of elliptic curves, Saito’s result, as
well as analysis of data on conductors and discriminants to determine whether patterns exist
between discriminant and conductor of elliptic curves. The researcher finds such patterns do
in fact exist and discusses two main patterns: that of the conductor dividing the discriminant
and that of the conductor ”branching” in a predictable way. These patterns also allow for
easier algorithms for computing conductors.