An explicit correspondence between certain modular curves

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2017-05-03
Authors/Contributors
Abstract
In this thesis, we recall an alternative proof of Merel's conjecture, which asserts that a certain explicit correspondence gives the isogeny relation between the Jacobians associated to the normalizer of split and non-split Cartan subgroups. This alternative proof does not require extensive representation theory and can be formulated in terms of certain finite geometries modulo $\ell$. Secondly, we generalize these arguments to exhibit an explicit correspondence which gives the isogeny relation between the Jacobians associated to split and non-split Cartan subgroups. An interesting feature is that the required explicit correspondence is considerably more complicated but can be expressed as a certain linear combination of double coset operators whose coefficients we are able to make explicit.
Document
Identifier
etd10163
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Copyright is held by the author.
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Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Chen, Imin
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