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

*The theory of numbers, from Ancient Greece to the 21st century*

(Slides for the 2024 Mahler public lecture)

pdf

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.

*An introduction to the categorical p-adic Langlands program*
(with Toby Gee and Eugen Hellmann)

pdf

*Explicit reciprocity laws and Iwasawa theory for modular forms*
(with Robert Pollack and Tom Weston)

pdf

* Localization of smooth p-power torsion representations of GL_2(Q_p)*
(with Andrea Dotto and Toby Gee)

pdf

* Moduli stacks of two-dimensional Galois representations *
(with Ana Caraiani, Toby Gee, and David Savitt)

pdf

* Local-global compatibility in the p-adic Langlands
programme for GL_2/Q *

(Draft dated March 23, 2011)

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* 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)

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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.)

* Moduli stacks of etale (phi,Gamma)-modules: a survey *
(with Toby Gee)

To appear in Proceedings of the International
Colloquium on Arithmetic Geometry, TIFR Mumbai, Janury 6-10, 2020.

pdf

* Moduli stacks of etale (phi,Gamma)-module and existence
of crystalline lifts *
(with Toby Gee)

Appeared in *Annals of Math. Studies* vol. 215, Princeton University Press,
2023.

pdf

Here is a list of errata.

* Langlands reciprocity: L-functions, automorphic forms, and Diophantine equations*

Appeared in *The genesis of the Langlands program*

(Julia Mueller, Freydoon Shahidi eds.),

London Mathematical Society Lecture Notes Series,
vol. 467, 2021, 301-386.

pdf

* Globally realizable components of local deformation rings*
(with Frank Calegari and Toby Gee)

Appeared in * J. Institut Math. Jussieu* 21 (2022), 533-602.

pdf

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

Appeared in * Alg. Geom.* 8 (2021), 1-132.

pdf

* On the density of supercuspidal points of fixed regular
weight in local deformation rings and global Hecke algebras *
(with Vytas Paskunas)

Appeared in *J. de l'Ecole Poly. Math.* 7 (2020), 337-371.

pdf

* Compatible systems of Galois representations associated to the
exceptional group E_6 *
(with George Boxer, Frank Calegari, Brandon Levin,
Keerthi Madapusi Pera, and Stefan Patrikis)

Appeared in * Forum Math. Sigma * 7 (2019), e4, 29 pages.

pdf

* Patching and the p-adic Langlands program for GL_2(Q_p)*
(with Ana Caraiani, Toby Gee, David Geraghty, Vytas Paskunas,
and Sug Woo Shin)

Appeared in *Comp. Math.* 154 (2018), no. 3, 503-548.

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* Explicit Serre weights for two-dimensional Galois representations*
(with Frank Calegari, Toby Gee, and Lambros Mavrides)

Appeared in * Comp. Math * 153 (2017), no. 9, 1893-1907.

pdf

* Patching and the p-adic local Langlands correspondence*
(with Ana Caraiani, Toby Gee, David Geraghty, Vytas Paskunas,
and Sug Woo Shin)

Appeared in *Camb. J. of Math.* 4 (2016), no. 2, 197-287.

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*Homological stability for completed homology *
(with Frank Calegari)

Appeared in *Math. Ann.* 364 (2016), no.3-4, 1025-1041.

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*p-adic Hodge-theoretic properties of etale cohomology
with mod p coefficients, and the cohomology of Shimura varieties*
(with Toby Gee)

Appeared in * Algebra and Number Theory* 9 (2015), no. 5, 1035-1088.

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pdf

* Lattices in the cohomology of Shimura curves*
(with Toby Gee and David Savitt)

Appeared in * Invent. Math. * 200 (2015), no. 1, 1-96.

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* Completed cohomology and the p-adic Langlands program*

Appeared in the Proceedings of the 2014 ICM.

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* 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.

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*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.

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* 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.

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* 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.

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* 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.

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* 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.

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* 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*.

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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.

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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).

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* 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.)

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* 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.

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* 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.

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

* Formal algebraic stacks*

pdf

*On the vanishing of certain extensions of admissible
smooth representations in characteristic p*

pdf

This very short note relates Gelfand--Kirillov dimensions,
duality, and extensions of representations.

* 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.)

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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.