{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/29346"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/29346","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Siegel modulator form (mod p) and algebraic modular forms","abstract":"In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre's result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) of genus g are the same as the ones given by algebraic modular forms (mod p) on the group GUg(B), as defined in [Gro99] and [Gro98]. The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties.","abstract_html":"In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre's result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) of genus g are the same as the ones given by algebraic modular forms (mod p) on the group GUg(B), as defined in [Gro99] and [Gro98]. The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties.","abstract_has_math":false,"creators":["Ghitza, Alexandru Edgar, 1976-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Aise Johan de Jong."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-22T22:20:50Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/29346","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Aise Johan de Jong."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mathematics"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/29346"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.","Includes bibliographical references (p. 101-104) and index."]},{"key":"dc:description.abstract","label":"Abstract","values":["In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre's result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) of genus g are the same as the ones given by algebraic modular forms (mod p) on the group GUg(B), as defined in [Gro99] and [Gro98]. The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Siegel modulator form (mod p) and algebraic modular forms"]}]}],"canonical_facts":{"dc:contributor.advisor":["Aise Johan de Jong."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics"],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Ghitza, Alexandru Edgar, 1976-"],"dc:date.accessioned":["2005-10-14T19:59:08Z"],"dc:date.available":["2005-10-14T19:59:08Z"],"dc:date.issued":["2003"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.","Includes bibliographical references (p. 101-104) and index."],"dc:description.abstract":["In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre's result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) of genus g are the same as the ones given by algebraic modular forms (mod p) on the group GUg(B), as defined in [Gro99] and [Gro98]. The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/29346"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Siegel modulator form (mod p) and algebraic modular forms"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:20:50Z"}