BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Stubley (UChicago) DTSTART:20200601T230000Z DTEND:20200601T235000Z DTSTAMP:20260423T022929Z UID:UCLA_NTS/5 DESCRIPTION:Title: Locally Split Galois Representations and Hilbert Modular Forms of Partial Weight One\nby Eric Stubley (UChicago) as part of UCLA Number Theory Seminar\n\n\nAbstract\nThe $p$-adic Galois representation attached to a $p $-ordinary eigenform is upper triangular when restricted to a decompositio n group at $p$. A natural question to ask is under what conditions this up per triangular decomposition splits as a direct sum. Ghate and Vatsal have shown that for the Galois representation attached to a Hida family of $p$ -ordinary eigenforms\, the restriction to a decomposition group at $p$ is split if and only if the family has complex multiplication\; in their proo f\, the weight one members of the family play a key role.\n\nI'll talk abo ut work in progress which aims to answer similar questions in the case of Galois representations for a totally real field which are split at only so me of the decomposition groups at primes above $p$. In this work Hilbert m odular forms of partial weight one play a central role\; I'll discuss what is known about them and to what extent the techniques of Ghate and Vatsal can be adapted to this situation.\n LOCATION:https://researchseminars.org/talk/UCLA_NTS/5/ END:VEVENT END:VCALENDAR