**SOME RECENT ARTICLES **

** **(updated February 18, 2018)

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

(**with H. Grobner, J. Lin): **Deligne's
conjecture for automorphic motives over CM-fields,

Part I: factorization. arXiv:1802.02958 [math.NT].

(**with H. Esnault): **Chern
classes of automorphic vector bundles, II.
arXiv:1801.08219
[math.AG].

(**with A.Venkatesh**): Derived Hecke algebra for weight one
forms, *Experimental Mathematics*,
Published online January 3, 2018, DOI: 10.1080/10586458.2017.1409144

(**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, in J. Cogdell,
J.-L. Kim, C.-B. Zhu, eds., *Representation
Theory, Number Theory, and Invariant Theory, In Honor of Roger Howe on the Occasion of His 70th Birthday*,
*Progress in Math*. **323** (2017) 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**,

p-adic and analytic properties of
period integrals and values of L-functions,**
Annales des MathŽmatiques du QuŽbec, 40(2)
**(2016) 435-452,

(**with H. Grobner, E. Lapid**) Whittaker regulators and non-critical
values of Asai L-functions, ** Contemporary Mathematics**,

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**,

(**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**,

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**,

*L*-functions and periods of adjoint motives, ** Algebra
and Number Theory**,

Beilinson-Bernstein localization
over **Q** and periods of automorphic
forms

** International Math. Research
Notices**,

The Taylor-Wiles method for
coherent cohomology, ** J.
Reine Angew. Math.**,

(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

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

** Arithmetic Geometry and
Automorphic Forms**,

Somerville: International
Press (**2011**): **pdf**

Arithmetic applications of the
Langlands program, ** Japanese J. Math.**,

**(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.**,

**(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

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

in *Algebra, Arithmetic, and
Geometry: Manin Festschrift*,** Progr. Math.**,

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 measure**, Documenta
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

**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

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)

**(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.**

**_______________________________________________________________________________________**

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

modular forms of half-integral
weight, 1987)**
**

**_______________________________________________________________________________________**