skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "EMERTON, MATTHEW"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, Journal of the Institute of Mathematics of Jussieu)
    Abstract Let $$n$$ be either  $$2$$ or an odd integer greater than  $$1$$ , and fix a prime  $p>2(n+1)$ . Under standard ‘adequate image’ assumptions, we show that the set of components of $$n$$ -dimensional $$p$$ -adic potentially semistable local Galois deformation rings that are seen by potentially automorphic compatible systems of polarizable Galois representations over some CM field is independent of the particular global situation. We also (under the same assumption on  $$n$$ ) improve on the main potential automorphy result of Barnet-Lamb et al.  [Potential automorphy and change of weight, Ann. of Math. (2)   179 (2) (2014), 501–609], replacing ‘potentially diagonalizable’ by ‘potentially globally realizable’. 
    more » « less
    Full Text Available 
  2. ; (, Algebraic Geometry)
    null (Ed.)
    Full Text Available 
  3. ; ; ; ; ; (, Forum of Mathematics, Sigma)
    We construct, over any CM field, compatible systems of $$l$$ -adic Galois representations that appear in the cohomology of algebraic varieties and have (for all $$l$$ ) algebraic monodromy groups equal to the exceptional group of type $$E_{6}$$ . 
    more » « less
    Full Text Available 
  4. ; ; ; (, Compositio Mathematica)
    We prove the explicit version of the Buzzard–Diamond–Jarvis conjecture formulated by Dembele et al. ( Serre weights and wild ramification in two-dimensional Galois representations , Preprint (2016), arXiv:1603.07708 [math.NT]). More precisely, we prove that it is equivalent to the original Buzzard–Diamond–Jarvis conjecture, which was proved for odd primes (under a mild Taylor–Wiles hypothesis) in earlier work of the third author and coauthors. 
    more » « less
    Full Text Available 
  5. ; (, Mathematische Annalen)
    Full Text Available