Skip to main content
MathOverflow

Return to Answer

corrected my name :-)
Source Link
David Loeffler
David Loeffler
  • 37k
  • 3
  • 89
  • 194

I felt that there couldn’t be such an isogeny, but when I saw @DavidLoefflere’s@DavidLoeffler’s answer, I realized that I had an argument, too. The formal group of the elliptic curve would be of height two, defined over $\mathbb Z_p$, but such things don’t have $p$-isogenies: the quotient formal group is definable only over a suitably ramified extension.

I felt that there couldn’t be such an isogeny, but when I saw @DavidLoefflere’s answer, I realized that I had an argument, too. The formal group of the elliptic curve would be of height two, defined over $\mathbb Z_p$, but such things don’t have $p$-isogenies: the quotient formal group is definable only over a suitably ramified extension.

I felt that there couldn’t be such an isogeny, but when I saw @DavidLoeffler’s answer, I realized that I had an argument, too. The formal group of the elliptic curve would be of height two, defined over $\mathbb Z_p$, but such things don’t have $p$-isogenies: the quotient formal group is definable only over a suitably ramified extension.

Source Link
Lubin
Lubin
  • 4.2k
  • 2
  • 27
  • 28

I felt that there couldn’t be such an isogeny, but when I saw @DavidLoefflere’s answer, I realized that I had an argument, too. The formal group of the elliptic curve would be of height two, defined over $\mathbb Z_p$, but such things don’t have $p$-isogenies: the quotient formal group is definable only over a suitably ramified extension.