BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rusiru Gambheera Arachchige (UCSD) DTSTART:20221027T210000Z DTEND:20221027T220000Z DTSTAMP:20260423T041157Z UID:UCSD_NTS/74 DESCRIPTION:Title: An unconditional equivariant main conjecture in Iwasawa theory\nby R usiru Gambheera Arachchige (UCSD) as part of UCSD number theory seminar\n\ nLecture held in APM 6402 and online.\n\nAbstract\nIn 2015 Greither and Po pescu constructed a new class of Iwasawa modules\, which are the number fi eld analogues of $p-$adic realizations of Picard 1- motives constructed by Deligne. They proved an equivariant main conjecture by computing the Fitt ing ideal of these new modules over the appropriate profinite group ring. This is an integral\, equivariant refinement of Wiles' classical main conj ecture. As a consequence they proved a refinement of the Brumer-Stark conj ecture away from 2. All of the above was proved under the assumption that the relevant prime $p$ is odd and that the appropriate classical Iwasawa $ \\mu$–invariants vanish. Recently\, Dasgupta and Kakde proved the Brumer -Stark conjecture\, away from 2\, unconditionally\, using a generalization of Ribet's method. We use the Dasgupta-Kakde results to prove an uncondit ional equivariant main conjecture\, which is a generalization of that of G reither and Popescu. As applications of our main theorem we prove a genera lization of a certain case of the main result of Dasgupta-Kakde and we com pute the Fitting ideal of a certain naturally arising Iwasawa module. This is joint work with Cristian Popescu.\n\npre-talk at 1:20\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/74/ END:VEVENT END:VCALENDAR