Resource type
Thesis type
(Thesis) M.Sc.
Date created
2017-05-03
Authors/Contributors
Author (aut): Salari Sharif, Parinaz
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
Copyright statement
Copyright is held by the author.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor (ths): Chen, Imin
Member of collection
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