Abelian surfaces with real multiplication over finite fields
| dc.contributor.author | Freese, Hilary, author | |
| dc.contributor.author | Achter, Jeffrey, advisor | |
| dc.contributor.author | Pries, Rachel, committee member | |
| dc.contributor.author | Peterson, Chris, committee member | |
| dc.contributor.author | Tavani, Daniele, committee member | |
| dc.date.accessioned | 2007-01-03T06:30:38Z | |
| dc.date.available | 2007-01-03T06:30:38Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | Given a simple abelian surface A/Fq, the endomorphism algebra, End(A) ⊗ Q, contains a unique real quadratic subfield. We explore two different but related questions about when a particular real quadratic subfield K+ is the maximal real subfield of the endomorphism algebra. First, we compute the number of principally polarized abelian surfaces A/Fq such that K+ ⊂ End(A) ⊗ Q. Second, we consider an abelian surface A/Q, and its reduction Ap = A mod p, then ask for which primes p is K+ ⊂ End(A) ⊗ Q. The result from the first question leads to a heuristic for the second question, namely that the number of p < χ for which K+ ⊂ End(A) ⊗ Q grows like √χ/log(c). | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Freese_colostate_0053A_12498.pdf | |
| dc.identifier.uri | http://hdl.handle.net/10217/83742 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | algebraic geometry | |
| dc.subject | number theory | |
| dc.title | Abelian surfaces with real multiplication over finite fields | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Freese_colostate_0053A_12498.pdf
- Size:
- 693.68 KB
- Format:
- Adobe Portable Document Format
- Description: