Divisor over ellitptic curves
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I struggle to prove the following theorem :
Let $E$ be an elliptic curve over a field $K$. Let $D=sum n_p P$ be a divisor on $E$. Then $D sim 0$ if and only if $sum [n_p]P=mathcal{O}$ where $mathcal{O}$ is the neutral for the group law of the curve.
elliptic-curves divisors-algebraic-geometry
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
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add a comment |
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I struggle to prove the following theorem :
Let $E$ be an elliptic curve over a field $K$. Let $D=sum n_p P$ be a divisor on $E$. Then $D sim 0$ if and only if $sum [n_p]P=mathcal{O}$ where $mathcal{O}$ is the neutral for the group law of the curve.
elliptic-curves divisors-algebraic-geometry
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
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1
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See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
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– ODF
Dec 22 '18 at 17:52
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Chapter ? Thank you !
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– Pierre21
Dec 22 '18 at 17:55
1
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Chapter III, sorry!
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– ODF
Dec 22 '18 at 17:56
$begingroup$
Thank you very much !
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– Pierre21
Dec 22 '18 at 18:00
add a comment |
$begingroup$
I struggle to prove the following theorem :
Let $E$ be an elliptic curve over a field $K$. Let $D=sum n_p P$ be a divisor on $E$. Then $D sim 0$ if and only if $sum [n_p]P=mathcal{O}$ where $mathcal{O}$ is the neutral for the group law of the curve.
elliptic-curves divisors-algebraic-geometry
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
$endgroup$
I struggle to prove the following theorem :
Let $E$ be an elliptic curve over a field $K$. Let $D=sum n_p P$ be a divisor on $E$. Then $D sim 0$ if and only if $sum [n_p]P=mathcal{O}$ where $mathcal{O}$ is the neutral for the group law of the curve.
elliptic-curves divisors-algebraic-geometry
elliptic-curves divisors-algebraic-geometry
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
asked Dec 22 '18 at 16:57
Pierre21Pierre21
1118
1118
1
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See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
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– ODF
Dec 22 '18 at 17:52
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Chapter ? Thank you !
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– Pierre21
Dec 22 '18 at 17:55
1
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Chapter III, sorry!
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– ODF
Dec 22 '18 at 17:56
$begingroup$
Thank you very much !
$endgroup$
– Pierre21
Dec 22 '18 at 18:00
add a comment |
1
$begingroup$
See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
$endgroup$
– ODF
Dec 22 '18 at 17:52
$begingroup$
Chapter ? Thank you !
$endgroup$
– Pierre21
Dec 22 '18 at 17:55
1
$begingroup$
Chapter III, sorry!
$endgroup$
– ODF
Dec 22 '18 at 17:56
$begingroup$
Thank you very much !
$endgroup$
– Pierre21
Dec 22 '18 at 18:00
1
1
$begingroup$
See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
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– ODF
Dec 22 '18 at 17:52
$begingroup$
See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
$endgroup$
– ODF
Dec 22 '18 at 17:52
$begingroup$
Chapter ? Thank you !
$endgroup$
– Pierre21
Dec 22 '18 at 17:55
$begingroup$
Chapter ? Thank you !
$endgroup$
– Pierre21
Dec 22 '18 at 17:55
1
1
$begingroup$
Chapter III, sorry!
$endgroup$
– ODF
Dec 22 '18 at 17:56
$begingroup$
Chapter III, sorry!
$endgroup$
– ODF
Dec 22 '18 at 17:56
$begingroup$
Thank you very much !
$endgroup$
– Pierre21
Dec 22 '18 at 18:00
$begingroup$
Thank you very much !
$endgroup$
– Pierre21
Dec 22 '18 at 18:00
add a comment |
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1
$begingroup$
See prop 3.4 & cor 3.5 in Silverman: pdmi.ras.ru/~lowdimma/BSD/Silverman-Arithmetic_of_EC.pdf
$endgroup$
– ODF
Dec 22 '18 at 17:52
$begingroup$
Chapter ? Thank you !
$endgroup$
– Pierre21
Dec 22 '18 at 17:55
1
$begingroup$
Chapter III, sorry!
$endgroup$
– ODF
Dec 22 '18 at 17:56
$begingroup$
Thank you very much !
$endgroup$
– Pierre21
Dec 22 '18 at 18:00