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The Atkin operator on spaces of overconvergent modular forms and arithmetic applications

Abstract:

We investigate the action of the Atkin operator on spaces of overconvergent p-adic modular forms. Our contributions are both computational and geometric. We present several algorithms to compute the spectrum of the Atkin operator, as well as its p-adic variation as a function of the weight. As an application, we explicitly construct Heegner-type points on elliptic curves. We then make a geometric study of the Atkin operator, and prove a potential semi-stability theorem for correspondences....

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Role:
Supervisor
Role:
Supervisor
Institution:
University of Oxford
Oxford college:
St Catherine's College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
Publication date:
2015
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
Oxford University, UK
URN:
uuid:081e4e46-80c1-41e7-9154-3181ccb36313
Local pid:
ora:11647

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