{"id":{"repo_id":"cuny-grad","oai_identifier":"oai:academicworks.cuny.edu:gc_etds-2341"},"canonical_url":"https://search.dev.ndltd.org/etd/cuny-grad/oai:academicworks.cuny.edu:gc_etds-2341","repository":{"repo_id":"cuny-grad","name":"City University of New York - Graduate Center","base_url":"https://academicworks.cuny.edu/do/oai/"},"display":{"title":"p-adic L-functions and the Geometry of Hida Families","abstract":"


A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using formal models. These methods should extend to the entire eigencurve.

","abstract_html":"<p><br />A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using formal models. These methods should extend to the entire eigencurve.</p>","abstract_has_math":true,"creators":["Kramer-Miller, Joseph"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Krzysztof Klosin"],"committee_chairs":[],"committee_members":["Krzysztof Klosin","Ken Kramer","Brooke Feigon"],"year":2016,"date_issued":"2016-06-03T07:00:00Z","date_published":"2016-06-03T07:00:00Z","updated_at":"2026-07-24T01:59:54Z","subjects":["Algebra","Number Theory","p-adic modular forms"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/1325","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Krzysztof Klosin"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Krzysztof Klosin","Ken Kramer","Brooke Feigon"]},{"key":"dc:creator","label":"Author","values":["Kramer-Miller, Joseph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-27T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebra","Number Theory","p-adic modular forms"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/1325"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["


A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using formal models. These methods should extend to the entire eigencurve.

"]},{"key":"dc:title","label":"Title","values":["p-adic L-functions and the Geometry of Hida Families"]}]}],"canonical_facts":{"dc:contributor.advisor":["Krzysztof Klosin"],"dc:contributor.committeemember":["Krzysztof Klosin","Ken Kramer","Brooke Feigon"],"dc:creator":["Kramer-Miller, Joseph"],"dc:date.available":["2016-04-27T07:00:00Z"],"dc:description.abstract":["


A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using formal models. These methods should extend to the entire eigencurve.

"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/1325"],"dc:subject":["Algebra","Number Theory","p-adic modular forms"],"dc:title":["p-adic L-functions and the Geometry of Hida Families"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:59:54Z"}