{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121395"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121395","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"D-modules, V-filtrations, and B-functions in mixed characteristic","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_has_math":false,"creators":["Kelm, Justin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dodd, Christopher","Katz, Sheldon","Heller, Jeremiah","Bradlow, Stephen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08","date_published":"2023-08","updated_at":"2026-07-22T22:24:57Z","subjects":["D-modules","V-filtrations","B-functions","Mixed Characteristic","Frobenius","Lifts Of Frobenius"],"languages":["en","eng"],"rights":["Copyright 2023 Justin Kelm"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121395","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dodd, Christopher","Katz, Sheldon","Heller, Jeremiah","Bradlow, Stephen"]},{"key":"dc:creator","label":"Author","values":["Kelm, Justin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-08","2023-05-05"]},{"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":["D-modules","V-filtrations","B-functions","Mixed Characteristic","Frobenius","Lifts Of Frobenius"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2023 Justin Kelm"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121395"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Justin Kelm, accepted the attached license on 2023-05-04 at 15:30.","The student, Justin Kelm, submitted this Dissertation for approval on 2023-05-04 at 15:37.","This Dissertation was approved for publication on 2023-05-05 at 11:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19336 on 2023-12-04 at 16:59:37","Within the existing literature, the theory of D-modules tends to bifurcate depending on whether the underlying based field is assumed to be of finite characteristic. The techniques used in either case may diverge greatly, but many results can be unified. In this paper we elaborate on this unification in the context of b-functions and V-filtrations by means of mixed characteristic arguments, emphasizing the role of Berthelot’s rings of differential operators as a translational tool. In particular, we present a proof in mixed characteristic of Kashiwara’s equivalence, give a definition in mixed characteristic of V-filtrations, and delineate the simultaneous eigenspace structure of said V-filtrations."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["D-modules, V-filtrations, and B-functions in mixed characteristic"]}]}],"canonical_facts":{"dc:contributor":["Dodd, Christopher","Katz, Sheldon","Heller, Jeremiah","Bradlow, Stephen"],"dc:creator":["Kelm, Justin"],"dc:date":["2023-08","2023-05-05"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Justin Kelm, accepted the attached license on 2023-05-04 at 15:30.","The student, Justin Kelm, submitted this Dissertation for approval on 2023-05-04 at 15:37.","This Dissertation was approved for publication on 2023-05-05 at 11:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19336 on 2023-12-04 at 16:59:37","Within the existing literature, the theory of D-modules tends to bifurcate depending on whether the underlying based field is assumed to be of finite characteristic. The techniques used in either case may diverge greatly, but many results can be unified. In this paper we elaborate on this unification in the context of b-functions and V-filtrations by means of mixed characteristic arguments, emphasizing the role of Berthelot’s rings of differential operators as a translational tool. In particular, we present a proof in mixed characteristic of Kashiwara’s equivalence, give a definition in mixed characteristic of V-filtrations, and delineate the simultaneous eigenspace structure of said V-filtrations."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121395"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Justin Kelm"],"dc:subject":["D-modules","V-filtrations","B-functions","Mixed Characteristic","Frobenius","Lifts Of Frobenius"],"dc:title":["D-modules, V-filtrations, and B-functions in mixed characteristic"],"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":"2026-07-22T22:24:57Z"}