Matthew Emerton's Papers and Preprints



All links are to dvi files or to pdf files, as indicated.

The following papers are either submitted for publication, or in the process of being revised prior to being submitted. New drafts may appear from time to time.

``Scheme-theoretic images'' of certain morphisms of stacks   (with Toby Gee)
pdf

Patching and the p-adic local Langlands correspondence   (with Ana Caraiani, Toby Gee, David Geraghty, Vytas Paskunas, and Sug Woo Shin)
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Local-global compatibility in the p-adic Langlands programme for GL_2/Q
(Draft dated March 23, 2011)
dvi pdf

On a class of coherent rings, with applications to the smooth representation theory of GL_2(Q_p) in characteristic p
(Draft dated May 19, 2008)
dvi pdf

The following papers have either appeared, or have been accepted to appear. For those papers that have appeared in print, the versions
presented here may differ slightly from the published versions. (For example, they don't always incorporate revisions made to proofs.)

Homological stability for completed homology   (with Frank Calegari)
To appear in Math. Ann.
dvi pdf

p-adic Hodge-theoretic properties of etale cohomology with mod p coefficients, and the cohomology of Shimura varieties   (with Toby Gee)
To appear in Algebra and Number Theory.
dvi pdf

Completed cohomology and the p-adic Langlands program
Appeared in the Proceedings of the 2014 ICM.
dvi pdf

Patching and the p-adic local Langlands correspondence Lattices in the cohomology of Shimura curves   (with Toby Gee and David Savitt)
Appeared in Invent. Math. 200 (2015), no. 1, 1-96.
dvi pdf

The local Langlands correspondence for GL(n) in families   (with David Helm)
Appeared in Ann. Sci. E.N.S. (4) 47 (2014), no. 4, 655-722.
pdf

A geometric perspective on the Breuil--Mezard conjecture   (with Toby Gee)
Appeared in J. Institut Math. Jussieu 13 (2014), no. 1, 183-223.
dvi pdf

Weight cycling and Serre-type conjectures for unitary groups  (with Toby Gee and Florian Herzig)
Appeared in Duke Math. J. 162 (2013), no. 9, 1649-1722.
dvi pdf

Completed cohomology --- A survey  (with Frank Calegari)
Appeared in Nonabelian Fundamental Groups and Iwasawa Theory
(John Coates, Minhyong Kim, Florian Pop, Mohamed Saidi, Peter Schneider eds.),
London Mathematical Society Lecture Notes Series, vol. 393, 2011, 239-257.
dvi pdf

Mod-p cohomology growth in p-adic analytic towers of 3-manifolds  (with Frank Calegari)
Appeared in Groups, Geometry, and Dynamics 5 (2011), 355-366.
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p-adic families of modular forms [after Hida, Coleman, and Mazur]
Appeared in Seminaire Bourbaki, 2009/2010, expose 1013, Asterisque 339 (2011), 31-61.
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On the effaceability of certain delta-functors  (with Vytas Paskunas)
Appeared in Asterisque 331 (2010), 439--447.
dvi pdf

Ordinary parts of admissible representations of p-adic reductive groups I. Definition and first properties
(Revised version, dated January 19, 2010)
Appeared in Asterisque 331 (2010), 335--381.
dvi pdf

Ordinary parts of admissible representations of p-adic reductive groups II. Derived functors
(Revised version, dated January 19, 2010)
Appeared in Asterisque 331 (2010), 383--438.
dvi pdf

Jacquet modules of locally analytic representations of p-adic reductive groups II. The relation to parabolic induction
(Draft dated October 10, 2007)
To appear in J. Institut Math. Jussieu.
dvi pdf

Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms   (with Frank Calegari)
Appeared in Ann. of Math. 170 (2009), 1437--1446
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Representations p-adique ordinaires de GL_2(Q_p) et compatibilite local-global   (with Christophe Breuil)
Appeared in Asterisque 331 (2010), 235--295.
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Elliptic curves of odd modular degree   (with Frank Calegari)
Appeared in Israel J. Math. 169 (2009), 417-444.
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Locally analytic representation theory of p-adic reductive groups: A summary of some recent developments
(Revised version, dated March 16, 2007)
Appeared in L-functions and Galois representations (D. Burns, K. Buzzard and J. Nekovar, eds.),
London Mathematical Society Lecture Note Series, vol. 320, 2007, 407-437.
dvi pdf

A local-global compatibility conjecture in the p-adic Langlands programme for GL_2/Q
Appeared in Pure and Applied Math. Quarterly 2 (2006), no. 2, 279-393.
(special issue in honour of John Coates' 60th birthday).
dvi pdf

Variation of Iwasawa invariants in Hida families   (with Robert Pollack and Tom Weston)
Appeared in Invent. Math. 163 (2006), no. 3, 523-580.
(The official electronic version can be found here on the SpringerLink website.)
dvi pdf

Jacquet modules of locally analytic representations of p-adic reductive groups I. Construction and first properties
Appeared in Ann. Sci. E.N.S. 39 (2006), no. 5, 775-839.
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p-adic L-functions and unitary completions of representations of p-adic reductive groups
Appeared in Duke Math. J. 130 (2005), no. 2, 353-392.
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On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
Appeared in Invent. Math. 164 (2006), no. 1, 1-84.
(The official electronic version can be found here on the SpringerLink website.)
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Locally analytic vectors in representations of locally p-adic analytic groups
(Revised version, dated September 19, 2011)
To appear in Memoirs of the AMS.
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On the ramification of Hecke algebras at Eisenstein primes   (with Frank Calegari)
Appeared in Invent. Math. 160 (2005), no. 1, 97-144.
(The official electronic version can be found here on the SpringerLink website.)
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A geometric Jacquet functor   (with David Nadler and Kari Vilonen)
Appeared in Duke Math. J. 125 (2004), no. 2, 267-278.
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An introduction to the Riemann-Hilbert correspondence for unit F-crystals   (with Mark Kisin)
Appeared in Geometric Aspects of Dwork Theory (A. Adolphson etc. eds.), Vol. II, Walter de Gruyter, 2004, 677-700.
dvi pdf

The Riemann-Hilbert correspondence for unit F-crystals   (with Mark Kisin)
Appeared in Asterisque 293 (2004).
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The Hecke algebra has large index   (with Frank Calegari)
Appeared in Math. Research Letters 11 (2004), no. 1, 125-137.
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Optimal quotients of modular Jacobians
Appeared in Math. Ann. 327 (2003), no. 3, 429-458.
(The official electronic version can be found here on the SpringerLink website.)
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Supersingular elliptic curves, theta series and weight two modular forms
Appeared in J. Amer. Math. Soc. 15 (2002), no. 3, 671-714.
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Unit L-functions and a conjecture of Katz   (with Mark Kisin)
Appeared in Ann. of Math. 153 (2001), no. 2, 329-354.
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The Eisenstein ideal in Hida's ordinary Hecke algebra
Appeared in IMRN 1999, No. 15, 793-802.
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A new proof of a theorem of Hida
Appeared in IMRN 1999, No. 9, 453-472.
dvi pdf

The following papers are ones which I do not intend to publish at the present time.

Deformations of Galois representations and applications --- talk at the IHP conference on the occassion of the Galois bicentennial
pdf
(These are more-or-less the notes of a talk I gave at the indicated conference. One thing I learned at the conference, from the talk of Bost,
and that I mentioned in my talk, but which is not included in the notes, is that some of the Galois theoretic aspects of the Taylor--Wiles
auxiliary primes were already noted in a letter of Jacobi in the 19th century. I find this thread, and other threads, of continuity in the
development of our subject very pleasing!)

A p-adic variational Hodge conjecture and modular forms with complex multiplication
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Extensions of crystalline representations   (with Mark Kisin)
(Note that this paper is unfinished, and will likely remain so in the future. The fourth section in particular requires some corrections.)
dvi

The following report gives an account of research undertaken by a working group at the American Insitute of Mathematics investigating the mod p local Langlands correspondence, during the workshop ``p-adic representations, modularity, and beyond'', held at AIM in February, 2006
pdf

In 1999 the IAS/Park City Mathematics Institute was devoted to arithmetic geometry.
I gave an informal lecture there introducing the subject of p-adic modular forms, a
write-up of which has been incorporated as an appendix to Fernando Gouvea's lecture
notes from the Insititute. Here is an early draft of this appendix (it is missing figures
and some corrections).
dvi
The final version is for sale here .

Here is a gzipped tar file which contains the various chapters (in postscript format)
of my Harvard doctoral thesis "2-adic modular forms of minimal slope".
emerton-thesis.tar.gz

If you are unsure what to do with a gzipped tar file, here are the directions.