{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/226462"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/226462","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction","abstract":"Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois group G = Gal(F[infinity]/Q). I show how the p[infinity]-Selmer group of E over F[infinity] controls the p[infinity]-Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules.","abstract_html":"Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois group G = Gal(F[infinity]/Q). I show how the p[infinity]-Selmer group of E over F[infinity] controls the p[infinity]-Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules.","abstract_has_math":false,"creators":["Lee, Chern-Yang"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-07-06","date_published":"2010-07-06","updated_at":"2026-07-22T22:24:04Z","subjects":["Iwasawa theory","Parity conjecture","Elliptic curves"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2bc5ccd0-2a67-4c95-92e7-637e674e7c13/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.16211","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Lee, Chern-Yang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2010-07-06"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["http://www.dspace.cam.ac.uk/handle/1810/226462","https://www.repository.cam.ac.uk/handle/1810/226462"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Iwasawa theory","Parity conjecture","Elliptic curves"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2bc5ccd0-2a67-4c95-92e7-637e674e7c13/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.16211"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/430c76f5-d061-449f-99e4-e0960bcb731e/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois group G = Gal(F[infinity]/Q). I show how the p[infinity]-Selmer group of E over F[infinity] controls the p[infinity]-Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["51a3714fc5adf9437971c3f830c8fa0d","48dcdf38f646da27e5e4bc6c1893d4fc"]},{"key":"dc:title","label":"Title","values":["Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction"]}]}],"canonical_facts":{"dc:creator":["Lee, Chern-Yang"],"dc:date.issued":["2010-07-06"],"dc:description.abstract":["Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], with Galois group G = Gal(F[infinity]/Q). I show how the p[infinity]-Selmer group of E over F[infinity] controls the p[infinity]-Selmer rank growth within the false Tate curve extension, and how it is connected to the root numbers of E twisted by absolutely irreducible orthogonal Artin representations of G, and investigate the parity conjecture for twisted modules."],"dc:format.checksum.md5":["51a3714fc5adf9437971c3f830c8fa0d","48dcdf38f646da27e5e4bc6c1893d4fc"],"dc:identifier.doi":["10.17863/CAM.16211"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/430c76f5-d061-449f-99e4-e0960bcb731e/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["http://www.dspace.cam.ac.uk/handle/1810/226462","https://www.repository.cam.ac.uk/handle/1810/226462"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2bc5ccd0-2a67-4c95-92e7-637e674e7c13/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Iwasawa theory","Parity conjecture","Elliptic curves"],"dc:title":["Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:04Z"}