A Radical Characterization of Abelian Varieties
| dc.contributor.author | Hui, Heung Shan Theodore | |
| dc.contributor.chair | Zywina, David J. | |
| dc.contributor.chair | Ramakrishna, Ravi Kumar | |
| dc.contributor.committeeMember | Speh, Birgit E M | |
| dc.date.accessioned | 2018-04-26T14:18:17Z | |
| dc.date.available | 2018-04-26T14:18:17Z | |
| dc.date.issued | 2017-08-30 | |
| dc.description.abstract | Let $A$ be a square-free abelian variety defined over a number field $K$. Let $S$ be a density one set of prime ideals $\p$ of $\mathcal{O}_K$. A famous theorem of Faltings says that the Frobenius polynomials $P_{A,\p}(x)$ for $\p\in S$ determine $A$ up to isogeny. We show that the prime factors of $|A(\FF_\p)|=P_{A,\p}(1)$ for $\p\in S$ also determine $A$ up to isogeny over an explicit finite extension of $K$. The proof relies on understanding the $\ell$-adic monodromy groups which come from the $\ell$-adic Galois representations of $A$, and the absolute Weyl group action on their weights. We also show that there exists an explicit integer $e\geq 1$ such that after replacing $K$ by a suitable finite extension, the Frobenius polynomials of $A$ at $\p$ must equal to the $e$-th power of a separable polynomial for a density one set of prime ideals $\p\subseteq\mathcal{O}_K$. | |
| dc.identifier.doi | https://doi.org/10.7298/X41V5C30 | |
| dc.identifier.other | Hui_cornellgrad_0058F_10398 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:10398 | |
| dc.identifier.other | bibid: 10361681 | |
| dc.identifier.uri | https://hdl.handle.net/1813/57004 | |
| dc.language.iso | en_US | |
| dc.subject | radical | |
| dc.subject | Galois representations | |
| dc.subject | Mathematics | |
| dc.subject | abelian varieties | |
| dc.subject | monodromy groups | |
| dc.title | A Radical Characterization of Abelian Varieties | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| 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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