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Patching and p-adic local Langlands

Connections for Women: New Geometric Methods in Number Theory and Automorphic Forms August 14, 2014 - August 15, 2014

August 14, 2014 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Ana Caraiani (Imperial College, London)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


The p-adic local Langlands correspondence is well understood for GL_2(Q_p), but appears much more complicated when considering GL_n(F), where either n>2 or F is a finite extension of Q_p. I will discuss joint work with Matthew Emerton, Toby Gee, David Geraghty, Vytautas Paskunas and Sug Woo Shin, in which we approach the p-adic local Langlands correspondence for GL_n(F) using global methods. The key ingredient is Taylor-Wiles-Kisin patching of completed cohomology. This allows us to prove many new cases of the Breuil-Schneider conjecture.

21320?type=thumb Caraiani 386 KB application/pdf Download
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H.264 Video 14040.mp4 316 MB video/mp4 rtsp://videos.msri.org/data/000/021/285/original/14040.mp4 Download
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