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The Breuil–Mézard conjecture when l≠p.

Shotton, Jack (2018) 'The Breuil–Mézard conjecture when l≠p.', Duke mathematical journal., 167 (4). pp. 603-678.


Let l and p be primes, let F=Qp be a finite extension with absolute Galois group GF , let F be a finite field of characteristic l, and let W GF ! GLn.F/ be a continuous representation. Let R./ be the universal framed deformation ring for . If l D p, then the Breuil–Mézard conjecture (as recently formulated by Emerton and Gee) relates the mod l reduction of certain cycles in R./ to the mod l reduction of certain representations of GLn.OF /. We state an analogue of the Breuil–Mézard conjecture when l ¤ p, and we prove it whenever l>2 using automorphy lifting theorems. We give a local proof when l is “quasibanal” for F and is tamely ramified. We also analyze the reduction modulo l of the types . / defined by Schneider and Zink.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Date accepted:26 July 2017
Date deposited:10 October 2018
Date of first online publication:23 December 2017
Date first made open access:10 October 2018

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