Anabelian Model Theory
| dc.contributor.author | Abdolahzadi, Romin | |
| dc.contributor.chair | Nerode, Anil | |
| dc.contributor.committeeMember | Moore, Justin Tatch | |
| dc.contributor.committeeMember | Kozen, Dexter | |
| dc.date.accessioned | 2022-10-31T16:19:43Z | |
| dc.date.available | 2022-10-31T16:19:43Z | |
| dc.date.issued | 2022-08 | |
| dc.description | 63 pages | |
| dc.description.abstract | We have codified the algebraic fundamental group of anabelian geometry as a multi-sorted logical structure so as to use model-theoretic ideas, analogies, and language to go further with the study of hyperbolic curves over number fields. Consequently, a definability analysis is now possible on smooth quasi-projective schemes and their algebraic fundamental groups in characteristic zero. We form a connection between the algebraic fundamental group and the Lascar group of a stable first-order theory of covering spaces. We then provide a formulation of a Grothendieck-type section conjecture in terms of pure stability. One such use-case, for finitely generated k, is the application of geometric stability theory to use elimination of imaginaries to construct k-rational points on hyperbolic k-curves. | |
| dc.identifier.doi | https://doi.org/10.7298/fbnz-sj50 | |
| dc.identifier.other | Abdolahzadi_cornellgrad_0058F_13130 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:13130 | |
| dc.identifier.uri | https://hdl.handle.net/1813/111907 | |
| dc.language.iso | en | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Algebraic geometry | |
| dc.subject | Anabelian geometry | |
| dc.subject | Logic | |
| dc.subject | Mathematics | |
| dc.subject | Model theory | |
| dc.subject | Number theory | |
| dc.title | Anabelian Model Theory | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810.2 | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Cornell University | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Mathematics |
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