Isogeny graphs, zero-cycles, and modular forms : computations over algebraic curves and surfaces
Abstract/Contents
- Abstract
- In the study of algebraic varieties over number fields or finite fields, there are many properties of these varieties that can be difficult to compute. This thesis discusses variants of the following three computational problems: (a) to compute an isogeny between two given supersingular elliptic curves; (b) to determine whether a zero-cycle on a product of elliptic curves is rationally equivalent to zero, and if so, to compute a rational equivalence; (c) to compute the space of cuspidal modular forms over a function field of genus greater than one. For each of these problems, we present algorithms that allow the problem to be solved in certain special cases, and prove results about these cases.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Love, Jonathan Richard |
|---|---|
| Degree supervisor | Vakil, Ravi |
| Degree supervisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Boneh, Dan, 1969- |
| Degree committee member | Boneh, Dan, 1969- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Jonathan Love. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/vw255ct2479 |
Access conditions
- Copyright
- © 2021 by Jonathan Richard Love
- License
- This work is licensed under a Creative Commons Attribution Share Alike 3.0 Unported license (CC BY-SA).
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