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Title: Selmer Groups And Ranks Of Hecke Rings
Authors: Lundell, Benjamin
Keywords: Galois Representations
Modular Forms
Hecke Rings
Issue Date: 31-May-2011
Abstract: In this work, we investigate congruences between modular cuspforms. Specifically, we start with a given cuspform and count the number of cuspforms congruent to it as we vary the weight or level. This counting problem is equivalent to understanding the ranks of certain completed Hecke rings. Using the deep modularity results of Wiles, et al., we investigate these Hecke rings by studying the deformation theory of the residual representation corresponding to our given cuspform. This leads us to consider certain Selmer groups attached to this residual representation. In this setting, we can apply standard theorems from local and global Galois cohomology to achieve our results.
Committee Chair: Ramakrishna, Ravi Kumar
Committee Member: Stillman, Michael Eugene
Sen, Shankar
Discipline: Mathematics
Degree Name: Ph.D. of Mathematics
Degree Level: Doctor of Philosophy
Degree Grantor: Cornell University
No Access Until: 2016-09-29
Appears in Collections:Cornell Theses and Dissertations

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