{"id":41673,"date":"2025-09-15T15:05:06","date_gmt":"2025-09-15T13:05:06","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/?post_type=core-researches&p=41673"},"modified":"2025-10-08T17:08:50","modified_gmt":"2025-10-08T15:08:50","slug":"kummer-theory","status":"publish","type":"core-researches","link":"https:\/\/www.uni.lu\/fstm-en\/core-researches\/kummer-theory\/","title":{"rendered":"Kummer theory for algebraic groups"},"content":{"rendered":"","protected":false},"excerpt":{"rendered":"","protected":false},"author":379,"featured_media":41674,"template":"","meta":{"featured_image_focal_point":{"x":0.58,"y":0.5},"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Kummer theory","uluxPrePostTitle":"Research project","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"rp_acronym":"Kummer theory for algebraic groups","rp_abstract":"Kummer theory is a classical and foundational mathematical theory that has been initiated in the 19th century by E. Kummer. It concerns algebraic field extensions that are obtained by adding radicals, provided that certain roots of unity are present in the base field. Perucca\u2019s research group has been investigating Kummer extensions over cyclotomic extensions, which means that one first adds the necessary roots of unity. By defining suitable divisibility parameters, Perucca and her team have described the degree and Galois group structure of these field extensions. The kind of fields that have been investigated in detail are number fields (especially quadratic and multiquadratic fields), p-adic fields, and function fields. \nIn recent years, Perucca's team and Olli J\u00e4rviniemi (University of Turku), Igor Shparlinski (University of New South Wales) and Pietro Sgobba (Xi\u2019an Jiaotong-Liverpool University) made progress on Artin's conjecture on primitive roots, mainly as an application of Kummer theory.\nSupported by Davide Lombardo (University of Pisa) and Pieter Bruin (University of Leiden), Perucca's research group also made progress in Kummer theory for abelian varieties. \nThe current research team investigating Kummer theory for algebraic groups consists in Perucca and her PhD students Alexandre Benoist (who started his PhD in December 2024) and Szabi Buzog\u00e1ny (who started his PhD in September 2025). Additionally, Perucca has a work in progress on Kummer theory for fields with Daniel Gil-Mu\u00f1oz (Charles University and University of Pisa).","rp_start_date":"2024-12-01 14:40:00","rp_duration":36,"rp_main_funder":"University of Luxembourg","rp_other_funders":["FNR"],"rp_external_partners":[],"rp_keywords":[],"rp_members":[{"name":"Antonella PERUCCA","isPI":true,"isExternal":false,"featuredImageUrl":"https:\/\/www.uni.lu\/en\/person-image\/NTAwMjg3OTZfX0FudG9uZWxsYSBQRVJVQ0NB","detailsPageUrl":"https:\/\/www.uni.lu\/fstm-en\/people\/antonella-perucca\/","id":"50028796"},{"name":"Alexandre BENOIST","isPI":true,"isExternal":false,"featuredImageUrl":"https:\/\/www.uni.lu\/en\/person-image\/NTAwNjc1MjNfX0FsZXhhbmRyZSBCRU5PSVNU","detailsPageUrl":"https:\/\/www.uni.lu\/fstm-en\/people\/alexandre-benoist\/","id":"50067523"},{"name":"Szabolcs BUZOGANY","isPI":true,"isExternal":false,"featuredImageUrl":"https:\/\/www.uni.lu\/en\/person-image\/NTAxMDAwMjRfX1N6YWJvbGNzIEJVWk9HQU5Z","detailsPageUrl":"https:\/\/www.uni.lu\/fstm-en\/people\/szabolcs-buzogany\/","id":"50100024"}]},"research-project-status":[275],"research-project-type":[267],"field-of-interest":[294],"organisation":[29],"authorship":[379],"acf":[],"_links":{"self":[{"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/core-researches\/41673"}],"collection":[{"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/core-researches"}],"about":[{"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/types\/core-researches"}],"author":[{"embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/users\/379"}],"version-history":[{"count":3,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/core-researches\/41673\/revisions"}],"predecessor-version":[{"id":42254,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/core-researches\/41673\/revisions\/42254"}],"wp:authorship":[{"embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/users\/379"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/media\/41674"}],"wp:attachment":[{"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/media?parent=41673"}],"wp:term":[{"taxonomy":"research-project-status","embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/research-project-status?post=41673"},{"taxonomy":"research-project-type","embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/research-project-type?post=41673"},{"taxonomy":"field-of-interest","embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/field-of-interest?post=41673"},{"taxonomy":"organisation","embeddable":true,"href":"https:\/\/www.uni.lu\/fstm-en\/wp-json\/wp\/v2\/organisation?post=41673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}