Ihara's lemma and multiplicity one
Abstract/Contents
- Abstract
- In this thesis, we formulate and prove a mod l multiplicity one result for spaces of automorphic forms on definite quaternion algebras over totally real fields, under some technical hypotheses so that Taylor's "Ihara avoidance" trick applies. We also explain how this can be used to deduce a special case of Ihara's lemma. To establish this multiplicity one result, we introduce a variant of the usual local deformation ring and calculate its Weil divisor class group using a strategy of Manning. A computation of its dualizing module then shows that this ring is Gorenstein. Finally, we construct a patched module from spaces of automorphic forms at different levels using the Taylor--Wiles--Kisin patching method and prove that it is free of rank one over a formal power series ring with coefficients in the local deformation ring.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Khu, Boon Hou Derek |
|---|---|
| Degree supervisor | Taylor, Richard |
| Thesis advisor | Taylor, Richard |
| Thesis advisor | Conrad, Brian |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Conrad, Brian |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Boon Hou Derek Khu. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/kj143ys6457 |
Access conditions
- Copyright
- © 2023 by Boon Hou Derek Khu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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