GALOIS EXTENSIONS and A CONJECTURE of OGG

Krzysztof Klosin, Mihran Papikian

Research output: Contribution to journalArticlepeer-review

Abstract

Let N = pq be a product of two distinct primes. There is an isogeny J0(N)new → JN defined over Q between the new quotient J0(N) and the Jacobian of the Shimura curve attached to indefinite quaternion algebra of discriminant N. In the case when p = 2, 3, 5, 7, 13, Ogg made predictions about the kernels of these isogenies. We show that Ogg's conjecture is false in general. Afterwards, we propose a strategy for proving results toward Ogg's conjecture in certain situations. Finally, we discuss this strategy in detail for N = 5• 13.

Original languageEnglish (US)
Pages (from-to)3821-3834
Number of pages14
JournalProceedings of the American Mathematical Society
Volume148
Issue number9
DOIs
StatePublished - Sep 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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