{"@context":"http://iiif.io/api/presentation/2/context.json","@type":"sc:Manifest","@id":"https://iiif.quartexcollections.com/wesleyan/iiif/1e0897e3-5fe9-423a-8ba8-ad9d82b664a9/manifest","label":"m2019-k18","metadata":[{"label":"Title","value":"Conditional bounds on heavenly elliptic curves over quadratic number fields"},{"label":"Subject","value":["Curves, Elliptic","Quadratic fields"]},{"label":"Rights","value":["In Copyright"]},{"label":"Repository","value":["University Archives"]},{"label":"Language","value":["English"]},{"label":"Item Information","value":"<a href=\"https://onesearch.wesleyan.edu/permalink/01CTW_WU/12cbh08/alma9932455163103768\" target=\"_blank\">M2019 K18</a>"},{"label":"Held By","value":"Wesleyan University Library, Wesleyan University, Middletown, CT, USA"},{"label":"Group","value":["Theses & Dissertations"]},{"label":"Name(s)","value":["Karpisz, Ryan J. (creator)"]},{"label":"Administrative Note","value":"Node ID: 16924<br>Administrative Notes: Old URL: https://wesscholar.wesleyan.edu/etd_mas_theses/240<br>Author Contact: ryankarpisz@gmail.com<br>Local Identifier: 240_karpisz_r_thesis<br>PID: ir:2515"},{"label":"Author-supplied Keywords","value":["Generalized riemann hypothesis","Conditional bounds","Rasmussen-Tamagawa conjecture","Elliptic curves"]},{"label":"Degree","value":["Master of Arts"]},{"label":"Description","value":"<p>Let  be a number field. An elliptic curve /is called <strong>heavenly</strong> at a rational prime ℓ if its ℓ-power torsion is constrained in a particular way. In 2008, Rasmussen and Tamagawa conjectured that there are only finitely many isomorphism classes of elliptic curves (and, more generally, abelian varieties) defined over  that are heavenly at some prime ℓ. They have since proven the conjecture in some unconditional cases; under the assumption of the Generalized Riemann Hypothesis, they have proven the conjecture in all cases. However, even in the conditional case, existing bounds are impractically large. We explain the new conditional result that for quadratic number fields  of small discriminant, if ℓ > 163, there are no elliptic curves  /  that are heavenly at ℓ.</p>"},{"label":"Digital Identifier","value":"m2019-k18"},{"label":"Thesis Advisor(s)","value":["Rasmussen, Christopher J."]},{"label":"Digital Object Identifier (DOI)","value":"https://doi.org/10.14418/wes01.2.245"},{"label":"Discipline","value":["Mathematics"]},{"label":"Date","value":"May 2019"},{"label":"EDTF Date","value":"D:00 M:00 Y:2019"},{"label":"Extent","value":"iv, 59 leaves ; 29 cm"},{"label":"File Format","value":["application/pdf"]},{"label":"Genre","value":["masters theses"]},{"label":"Digital Origin","value":["born digital"]},{"label":"Type","value":["Text"]}],"description":"Conditional bounds on heavenly elliptic curves over quadratic number 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