{"id":2210,"date":"2021-08-22T12:19:15","date_gmt":"2021-08-22T19:19:15","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=2210"},"modified":"2021-10-23T19:24:30","modified_gmt":"2021-10-24T02:24:30","slug":"antc-seminar-pavel-guerzhoy-university-of-hawaii-2","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/","title":{"rendered":"Damerell&#8217;s theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii)"},"content":{"rendered":"<div>It is widely believed that Weierstrass ignored Eisenstein&#8217;s theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. In particular, the Eisenstein series of weight two does not converge absolutely while Eisenstein&#8217;s theory assigned a value to this series.<\/div>\n<div><\/div>\n<div>It is now well-known that the quantity which Eisentsein assigned to this series is not only correct, but it has interesting\u00a0interpretations and attracted much attention. It has been proved by Damerell in 1970 that this quantity is an algebraic number if the underlying elliptic curve has complex multiplication.<\/div>\n<div><\/div>\n<div>In 1976, N. Katz interpreted Damerell&#8217;s theorem in terms of DeRham cohomology; that allowed for a p-adic approach to this algebraic number. This p-adic version of Damerell&#8217;s theorem was instrumental in Katz&#8217;s theory of p-adic modular forms and p-adic L-functions of CM-fields. The approach, by design, works for those primes which split in the CM-field.<\/div>\n<div><\/div>\n<div>In this talk, we offer a modification of Katz&#8217; p-adic approach to the weight two Eisenstein series which works uniformly well for all primes of good reduction, both inert and splitting in the CM-field.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>It is widely believed that Weierstrass ignored Eisenstein&#8217;s theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. In particular, the Eisenstein [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":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,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-2210","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Damerell&#039;s theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii) - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Damerell&#039;s theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"It is widely believed that Weierstrass ignored Eisenstein&#8217;s theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. In particular, the Eisenstein [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T02:24:30+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/\",\"name\":\"Damerell's theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2021-08-22T19:19:15+00:00\",\"dateModified\":\"2021-10-24T02:24:30+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\/\/colleges.claremont.edu\/ccms\/events\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Damerell&#8217;s theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/colleges.claremont.edu\/ccms\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Damerell's theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii) - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-pavel-guerzhoy-university-of-hawaii-2\/","og_locale":"en_US","og_type":"article","og_title":"Damerell's theorem: p-adic version, supersingular case (Pavel Guerzhoy, University of Hawaii) - Claremont Center for the Mathematical Sciences","og_description":"It is widely believed that Weierstrass ignored Eisenstein&#8217;s theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. 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