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148(3): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)22:08 ID:hRRJMwM+(1/6) AAS
>>139
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導手：Conductor of an elliptic curve

外部ﾘﾝｸ:en.wikipedia.org
Conductor of an elliptic curve
(抜粋)
Contents
省14

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149(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)22:22 ID:hRRJMwM+(2/6) AAS
>>148 追加

外部ﾘﾝｸ:en.wikipedia.org
Tate's algorithm
(抜粋)
In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve E over {\displaystyle \mathbb {Q} }\mathbb {Q} , or more generally an algebraic number field, and a prime or prime ideal p. It returns the exponent fp of p in the conductor of E, the type of reduction at p, the local index
c_p=[E(Q_p):E^0(Q_p)],
where E^0(Q_p) is the group of Q_p-points whose reduction mod p is a non-singular point.
省10

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150: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)22:26 ID:hRRJMwM+(3/6) AAS
>>148
>Serre & Tate (1968) extended the theory to conductors of abelian varieties.

これだな
外部ﾘﾝｸ:en.wikipedia.org
Conductor of an abelian variety
(抜粋)
In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad reduction at some prime is.
省1

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151(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)23:21 ID:hRRJMwM+(4/6) AAS
>>148 追加

外部ﾘﾝｸ:mathoverflow.net
<mathoverflow>
Definition and meaning of the conductor of an elliptic curve
(抜粋)
I never really understood the definition of the conductor of an elliptic curve.
asked Oct 23 '09 at 3:15
省12

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152: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)23:28 ID:hRRJMwM+(5/6) AAS
>>151 追加

外部ﾘﾝｸ:www.lmfdb.org
LMFDB
Conductor of an elliptic curve (reviewed)
(抜粋)
The conductor of an elliptic curve E defined over a number field K is an ideal of the ring of integers of K that is divisible by the prime ideals of bad reduction and no others.

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153: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/15(水)23:41 ID:hRRJMwM+(6/6) AAS
>>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
外部ﾘﾝｸ[cgi]: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
省12

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