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.
Ordinary parts of admissible representations of p-adic reductive
groups I. Definition and first properties
(Revised version, dated March 7, 2008)
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Ordinary parts of admissible representations of p-adic reductive
groups II. Derived functors
(Draft dated October 4, 2007)
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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.)
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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Bounds for multiplicities of unitary representations of
cohomological type in spaces of cusp forms (with Frank Calegari)
To appear in Ann. of Math.
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Representations p-adique ordinaires de GL_2(Q_p) et compatibilite
local-global (with Christophe Breuil)
To appear in Asterisque.
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Elliptic curves of odd modular degree (with Frank Calegari)
To appear in Israel J. Math.
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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.~Nekov\'a\v r, eds.),
London Mathematical Society Lecture Note Series,
vol.~320, 2007, 407--437.
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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 October 16, 2004)
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.
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
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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).
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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.