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                                SOME RECENT ARTICLES

                                                      (updated February 1, 2017)

 

    Published articles may differ slightly from the versions on this page.

 

 

 

 

(with F. Calegari, D. Geraghty):  Bloch-Kato conjectures for automorphic motives: pdf

 

(with H. Esnault):  Chern classes of automorphic vector bundles, Pure and Applied Mathematics Quarterly, to appear. arXiv:1701.09073 [math.AG].

 

(with J. Lin):  Period relations and special values of Rankin-Selberg L-functions, to appear in Contemporary Math., special issue in honor of Roger Howe (2016), arxiv.org/abs/1608.07527 [math.NT].

 

(with G. Bšckle, C. Khare, J. Thorne):  G^-local systems on smooth projective curves are potentially automorphic, arXiv:1609.03491 [math.NT]

 

(with E. Eischen, J.-S. Li, C. Skinner):  p-adic L-functions for unitary Shimura varieties, II; zeta integral calculations, III :  ordinary families and p-adic L-functions, arXiv: 1602.01776 [math.NT]

 

Speculations on the mod p representation theory of p-adic groups, Annales de la FacultŽ des sciences de Toulouse, ,  25, (2016) 403-418, special issue in honor of V. Schechtman: pdf

 

p-adic and analytic properties of period integrals and values of L-functions, Annales des MathŽmatiques du QuŽbec,  40(2) (2016) 435-452, special issue in honor of Glenn Stevens: pdf

 

(with H. Grobner, E. Lapid) Whittaker regulators and non-critical values of Asai L-functions, Contemporary Mathematics, 664 (2016) 119-134.  http://arxiv.org/abs/1408.1840v2

 

Automorphic Galois representations and Shimura varieties, Proceedings of the ICM 2014: pdf

 

(with H. Grobner)  Whittaker periods, motivic periods, and special values of tensor product L-functions Journal of the Institut de MathŽmatiques de Jussieu, 15 (2016) 711-769: pdf

 

(with K.-W. Lan, R. Taylor, and J. Thorne)  On the rigid cohomology of certain Shimura varieties :  Research in the Mathematical Sciences, Special Collection in honor of Robert Coleman,  3: 39, (2016):  pdf

 

Testing rationality of coherent cohomology of Shimura varieties, in J. Cogdell et al., eds,

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro,

                  Contemporary Mathematics, 614, 81-96 (2014): pdf

 

Weight zero Eisenstein cohomology of Shimura varieties via Berkovich spaces, Pacific J. Math.

                        (supplement to special issue in memory of J. Rogawski), 268, 275-81 (2014) pdf

 

(with G. Chenevier)  Construction of automorphic Galois representations, II,

Cambridge Journal of Mathematics, 1, 57-73 (2013) :  pdf

 

L-functions and periods of adjoint motives, Algebra and Number Theory, 7 (2013), 117-155pdf

 

Beilinson-Bernstein localization over Q and periods of automorphic forms

International Math. Research Notices, 2013, 2000-2053 (2013)pdf (this is an uncorrected version, with different numbering than the published version; erratum in preparation)

 

The Taylor-Wiles method for coherent cohomology,  J. Reine Angew. Math., 679 125-153 (2013):  pdf 

    (Readers are warned that the notation may not be entirely consistent in this preliminary draft.)

 

(with T. Barnet-Lamb, D. Geraghty, and R. Taylor) A family of Calabi-Yau varieties and

potential automorphy, II,  Proc. RIMS, 47, 29-98 (2011):  pdf

 

(with J.-S. Li and B. Sun) Theta correspondences for close unitary groups, in

Arithmetic Geometry and Automorphic Forms, Advanced Lectures in Mathematics, 19,

Somerville:  International Press (2011):  pdf

 

Arithmetic applications of the Langlands program, Japanese J. Math., 3rd series, 5, 1-71 (2010):  pdf

 

(with R. Guralnick and N. Katz) Automorphic realization of residual Galois representations,

J. Eur. Math. Soc.  12,  915-937  (2010):  pdf

 

(with N. Shepherd-Barron and R. Taylor)  A family of Calabi-Yau varieties and potential

automorphy, Annals of Math.171,  779-813  (2010):  pdf

 

(with L. Clozel and R. Taylor) Automorphy for some l-adic lifts of automorphic mod l representations


(version of June 2008)Publ. Math. IHES, 108, 1-181 (2008):  pdf

 

Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications,  

in Algebra, Arithmetic, and Geometry:  Manin Festschrift, Progr. Math., 270, 1-21

Boston:  BirkhŠuser (2009): pdf

 

Cohomological automorphic forms on unitary groups, II:  Period relations and values of L-functions, 

in Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory,

Vol. 12, Lecture Notes Series, Institute of Mathematical Sciences, National University of

Singapore (volume in honor of Roger Howe): pdf

 

(with J.-S. Li and C. Skinner)  p-adic L-functions for unitary Shimura varieties, Part I:  construction

of the Eisenstein measureDocumenta Math., Extra Volume:  John H. Coates' Sixtieth Birthday

393-464 (2006):  pdf

 

A simple proof of rationality of Siegel-Weil Eisenstein series, in W.T. Gan, S. S. Kudla, and

Y. Tschinkel, eds., Eisenstein Series and Applications, BirkhŠuser:  Progress in Mathematics

258, 149-186 (2008):  pdf

    Appendix by Paul Garrett:  Archimedean zeta integrals for unitary groups

 

(with J.-S. Li and C. Skinner)  The Rallis inner product formula and p-adic L-functions, in

Automorphic Representations, L-functions and Applications:  Progress and Prospects,

Berlin:  de Gruyter,  225-255 (2005) (volume in honor of S. Rallis)dvi

 

The Local Langlands correspondence: Notes of (half) a course at the IHP, Spring 2000, 
AstŽrisque, 298, 17-145 (2005) pdf.
   

The argument on p. 130-131 is only valid for split groups:  see explanation here.

 

(with J.-P. Labesse)  Conditional base change for unitary groups, Asian J. Math.  8,  
653-684 (2004):  pdf

 

Occult period invariants and critical values of the degree four $L$-function of $GSp(4)$,  in 


H. Hida, D. Ramakrishnan, F. Shahidi, eds.,   Contributions to automorphic forms, geometry, 


and number theory (volume in honor of J. Shalika), 331-354 (2004):    pdf

 

(with S. S. Kudla)  On a conjecture of Jacquet,  in H. Hida, D. Ramakrishnan, F. Shahidi, eds.,  

Contributions to automorphic forms, geometry, and number theory (volume in honor of J. Shalika),

355-371 (2004):  dvi

 

(with S. Zucker)  Boundary cohomology of Shimura varieties, III:  The nightmare continues, 


MŽmoires de la Soc. Math. France,  85 (2001):  dvi

 

(with R. Taylor)  Deformations of automorphic Galois representations, fourth preliminary draft, 2003: 
dvi

This is the fourth draft of a manuscript originally written in 1998, most of which has been

 
incorporated into the joint paper of the two authors with L. Clozel.

 

(with R. Taylor)  Regular models of certain Shimura varieties, Asian J. Math. 6, 61-94 (2002):  dvi

 

(with R. Taylor)  On the geometry and cohomology of some Shimura varieties, 

Annals of Math. 
Studies 151, Princeton University Press (2001).

 

Local Langlands correspondences and vanishing cycles on Shimura varieties,

Proceedings of the 
European Congress of Mathematics, Barcelona, 2000;

Progress in Mathematics, 201, 
Basel:  BirkhaŸser Verlag, 407-427 (2001):  dvi    

There is a mistake in the statement of Proposition 4.1 (ii) and in Conjecture 5.2:  see explanation here.

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Arithmetic of the oscillator representation  (unpublished manuscript on the arithmetic of Siegel

modular forms of half-integral weight, 1987)

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