{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86856"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86856","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the Modularity of Higher-Dimensional Varieties","abstract":"In this thesis, we first introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we show that a quintic threefold with 4-dimensional middle cohomology is Hilbert modular. This answers a question of Consani & Scholten. Let rho : Gal( Q/Q&parl0; 5&parr0; ) → GL4( Q2&parl0; 5&parr0; ) be the representation on H3( X, Q2&parl0;5 &parr0; ). We show that rho corresponds to (f, f sigma), where f is a newform over Q5 of weight (2, 4) and level 30, and sigma is the nontrivial element in the Galois group Gal( Q&parl0;5&parr0;/ Q ).","abstract_html":"In this thesis, we first introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we show that a quintic threefold with 4-dimensional middle cohomology is Hilbert modular. This answers a question of Consani & Scholten. Let rho : Gal( Q/Q&parl0; 5&parr0; ) → GL4( Q2&parl0; 5&parr0; ) be the representation on H3( X, Q2&parl0;5 &parr0; ). We show that rho corresponds to (f, f sigma), where f is a newform over Q5 of weight (2, 4) and level 30, and sigma is the nontrivial element in the Galois group Gal( Q&parl0;5&parr0;/ Q ).","abstract_has_math":false,"creators":["Yi, You-Chiang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Boston, Nigel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:53Z","date_published":"2015-09-28T15:19:53Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3199188"],"render_values":[{"text":"(MiAaPQ)AAI3199188","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86856","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Boston, Nigel"]},{"key":"dc:creator","label":"Author","values":["Yi, You-Chiang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:53Z","10000-01-01","2005"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86856","(MiAaPQ)AAI3199188"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we first introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we show that a quintic threefold with 4-dimensional middle cohomology is Hilbert modular. This answers a question of Consani & Scholten. Let rho : Gal( Q/Q&parl0; 5&parr0; ) → GL4( Q2&parl0; 5&parr0; ) be the representation on H3( X, Q2&parl0;5 &parr0; ). We show that rho corresponds to (f, f sigma), where f is a newform over Q5 of weight (2, 4) and level 30, and sigma is the nontrivial element in the Galois group Gal( Q&parl0;5&parr0;/ Q ).","Made available in DSpace on 2015-09-28T15:19:53Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3199188.pdf: 2400809 bytes, checksum: 92bee265aed2d4cd7f7c60f3610ff2bf (MD5) Previous issue date: 2005","Embargo set by: Seth Robbins for item 88137 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","91 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005."]},{"key":"dc:title","label":"Title","values":["On the Modularity of Higher-Dimensional Varieties"]}]}],"canonical_facts":{"dc:contributor":["Boston, Nigel"],"dc:creator":["Yi, You-Chiang"],"dc:date":["2015-09-28T15:19:53Z","10000-01-01","2005"],"dc:description":["In this thesis, we first introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we show that a quintic threefold with 4-dimensional middle cohomology is Hilbert modular. This answers a question of Consani & Scholten. Let rho : Gal( Q/Q&parl0; 5&parr0; ) → GL4( Q2&parl0; 5&parr0; ) be the representation on H3( X, Q2&parl0;5 &parr0; ). We show that rho corresponds to (f, f sigma), where f is a newform over Q5 of weight (2, 4) and level 30, and sigma is the nontrivial element in the Galois group Gal( Q&parl0;5&parr0;/ Q ).","Made available in DSpace on 2015-09-28T15:19:53Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3199188.pdf: 2400809 bytes, checksum: 92bee265aed2d4cd7f7c60f3610ff2bf (MD5) Previous issue date: 2005","Embargo set by: Seth Robbins for item 88137 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","91 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005."],"dc:identifier":["http://hdl.handle.net/2142/86856","(MiAaPQ)AAI3199188"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["On the Modularity of Higher-Dimensional Varieties"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}