BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Samit Dasgupta (Duke) DTSTART:20230511T210000Z DTEND:20230511T220000Z DTSTAMP:20260423T022732Z UID:UCSD_NTS/93 DESCRIPTION:Title: Ribet’s Lemma\, the Brumer-Stark Conjecture\, and the Main Conjecture< /a>\nby Samit Dasgupta (Duke) as part of UCSD number theory seminar\n\nLec ture held in APM 6402 and online.\n\nAbstract\nIn 1976\, Ken Ribet used mo dular techniques to prove an important relationship between class groups o f cyclotomic fields and special values of the zeta function. Ribet’s me thod was generalized to prove the Iwasawa Main Conjecture for odd primes p by Mazur-Wiles over Q and by Wiles over arbitrary totally real fields. \ n\nCentral to Ribet’s technique is the construction of a nontrivial exte nsion of one Galois character by another\, given a Galois representation s atisfying certain properties. Throughout the literature\, when working in tegrally at p\, one finds the assumption that the two characters are not c ongruent mod p. For instance\, in Wiles’ proof of the Main Conjecture\, it is assumed that p is odd precisely because the relevant characters mig ht be congruent modulo 2\, though they are necessarily distinct modulo any odd prime.\n\nIn this talk I will present a proof of Ribet’s Lemma in t he case that the characters are residually indistinguishable. As arithmet ic applications\, one obtains a proof of the Iwasawa Main Conjecture for t otally real fields at p=2. Moreover\, we complete the proof of the Brumer -Stark conjecture by handling the localization at p=2\, building on joint work with Mahesh Kakde for odd p. Our results yield the full Equivariant Tamagawa Number conjecture for the minus part of the Tate motive associate d to a CM abelian extension of a totally real field\, which has many impor tant corollaries.\n\nThis is joint work with Mahesh Kakde\, Jesse Silliman \, and Jiuya Wang.\n\npre-talk at 1:20pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/93/ END:VEVENT END:VCALENDAR