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SUMMARY:On the automorphy of 2-dimensional potentially semistable deformat
 ion rings of $G_{Q_p}$ - Shen-Ning Tung (Universität Duisburg-Essen)
DTSTART:20180522T133000Z
DTEND:20180522T143000Z
UID:TALK105412@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Using p-adic local Langlands correspondence for GL2(Qp)\, we p
 rove that the support of patched modules constructed by Caraiani\, Emerton
 \, Gee\, Geraghty\, Paskunas\, and Shin meet every irreducible component o
 f the potentially semistable deformation ring. This gives a new proof of t
 he Breuil-Mézard conjecture for 2-dimensional representations of the abso
 lute Galois group of Qp when p>2\, which is new in the case p=3 and $\\bar
 {r}$ a twist of an extension of the trivial character by the mod p cycloto
 mic character. As a consequence\, a local restriction in the proof of Font
 aine-Mazur conjecture by Kisin is removed.
LOCATION:MR13
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