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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2013
    • (edited Jul 17th 2013)

    stub for isogeny

  1. I found a more conceptual explanation of isogenies and reformulated the entry to include it.

    Anonymous

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 3rd 2018

    Charles Rezk speaks of isogenies of formal groups in his ICM talk. What’s the story about all the kinds of entity the term applies to?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 3rd 2018

    Hmm, that modification announced in #2 hasn’t helped, has it?

    What Urs has in v2 was fine. An elliptic curve is just a kind of algebraic group. The definition of isogeny as a surjection with finite kernel applies to the larger notion.

  2. Author of the modification speaking. I just felt that "surjection with finite kernel" was not a conceptually satisfying notion. Why would that be a good equivalence relation? "Rational group homomorphism" on the other hand makes sense and it is well-understood why rational equivalence is important. The two notions are equivalent for abelian varieties, which is the most important case, and I don't think isogenies are of much use outside of that. But I'll rewrite it to derive the second notion from the first.
  3. This better?

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 3rd 2018
    • (edited Oct 3rd 2018)

    That’s looking good. Thanks!

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