Earlier papers of David Harbater

Deformation theory and the fundamental group in algebraic geometry.  
    Ph.D. thesis, M.I.T., May 1978.
Deformation theory and the tame fundamental group.  Transactions
    of the AMS, vol. 262 (1980), pp. 399-415.
Moduli of p-covers of curves, Communications in Algebra, 8 (12)
    (1980), pp. 1095-1122.
Convergent arithmetic power series, Amer. J. Math., 106 (1984),
    no. 4, pp. 801-846.
Ordinary and supersingular covers in characteristic p , Pacific
    J. Math., 113 (1984) no. 2, pp. 349-363.
Mock covers and Galois extensions, Journal of Algebra, 91 (1984),
    pp. 281-293.
Algebraic rings of arithmetic power series, Journal of Algebra,
    91 (1984), pp. 294-319.
Hurwitz families and arithmetic Galois groups (with K. Coombes),
    Duke Mathematical Journal, 52 (1985), pp. 821-839.
Galois coverings of the arithmetic line, in Number Theory:  New
    York, 1984-85.  Springer LNM, vol. 1240 (1987), pp. 165-195.
Galois covers of an arithmetic surface, American Journal of
    Mathematics, 110 (1988), no. 5, pp. 849-885.
Every curve is a Hurwitz space (with S. Diaz and R. Donagi), Duke
    Mathematical Journal, 59 (1989), pp. 737-746.
Global approximation in dimension two (with J. Denef), Journal of
    Algebra, 129 (1990), pp. 159-193.
Strong Bertini theorems, (with S. Diaz), Transactions of the AMS, 
    324 (1991), 73-86.
On purity of inertia, Proceedings of the AMS, 112 (1991), 311-319.
Potential theory over local and global fields:  I, Journal of
    Algebra, 148 (1992), 337-383.
Potential theory over local and global fields:  II,  Journal of
    Algebra, 148 (1992), 384-432.
Arithmetic discriminants and horizontal intersections,
    Mathematische Annalen, 291 (1991), 705-724.

Formal patching and adding branch points, American Journal of Mathematics, 
   115 (1993), 487-508.

Abhyankar's conjecture on Galois groups over curves, Inventiones Math., 
   117 (1994), 1-25.
Galois groups with prescribed ramification, in "Proceedings of a      
   Conference on Arithmetic Geometry" (Arizona State Univ., 1993), AMS 
   Contemporary Mathematics Series, vol. 174, 1994, pp. 35-60.
   pdf file
Fundamental groups and embedding problems in characteristic p, in    
   "Recent Developments in the Inverse Galois Problem" (M. Fried, et al,  
   eds.), AMS Contemporary Mathematics Series, vol. 186, 1995, pp.353-369.
   pdf file

Fundamental groups of curves in characteristic p, in "Proceedings of the    
   International Congress of Mathematicians" (Zurich, 1994), Birkhauser,
   1995, pp.656-666.
   pdf file

Approximating Galois orbits of dessins (with L. Schneps), in "Geometric
   Galois Actions", Volume I, London Mathematical Society Lecture Note
   series, vol. 242, Cambridge University Press, 1997, pp.205-230.
   pdf file

Fields of definition of p-adic covers (with P. Debes), Crelle's Journal,
   vol. 498 (1998), 223-236.
   pdf file

Patching and thickening problems (with K. Stevenson), J. Alg., vol. 212
   (1999), 272-304.
   pdf file 

Embedding problems and adding branch points, in "Aspects of Galois
   Theory", London Mathematical Society Lecture Note series, vol. 256,
   Cambridge University Press, 1999, pp.119-143.
   pdf file
Fundamental groups of moduli and the Grothendieck-Teichmuller group 
   (with L. Schneps), Trans. AMS, vol. 352 (2000), 3117-3148. 
   pdf file

Embedding problems with local conditions, Israel Journal of Mathematics,
   vol. 118 (2000), 317-355.
   pdf file of paper 
   pdf file of correction/addendum 

Valued fields and covers in characteristic p (with M. van der Put,
   and with an appendix by R. Guralnick), in "Valuation Theory and its
   Applications", Fields Institute Communications, vol.32,  
   ed. by F.-V. Kuhlmann, S. Kuhlmann and M. Marshall, 2002, pp.175-204. 
   pdf file

Generalizations of Abhyankar's Conjecture.  Appendix to Desingularization
   and modular Galois theory, by S.S. Abhyankar, in "Arithmetic 
   Fundamental Groups and Noncommutative Algebra" (M.Fried, ed.), 
   AMS, PSPUM vol.70, 2002, pp.443-447.
   pdf file

Shafarevich conjecture.  In Supplement III, Encyclopaedia of Mathematics.
   Managing Editor: M. Hazewinkel, Kluwer Academic Publishers, 2002,
   pdf file

Abhyankar's Conjecture and embedding problems, Crelle's Journal,
   vol. 559 (2003), 1-24.
   pdf file
   (Also see related correction/addendum to 2000 Is.J. paper.)

Abhyankar's local conjecture on fundamental groups (with K. Stevenson),
   in "Algebra, Arithmetic and Geometry with Application" (Abhyankar 70th 
   birthday conference proceedings, C.Christensen et al., eds.), 
   Springer-Verlag, 2003, pp. 473-485.
   pdf file

Patching and Galois theory.  In "Galois Groups and Fundamental Groups" 
   (L. Schneps, ed.), MSRI Publications series, vol.41,
   Cambridge University Press, 2003, pp.313-424.
   Long pdf file of the whole paper;
   or two shorter pdf files: part 1 and part 2
Local Galois theory in dimension two (with K. Stevenson), Advances in 
   Math. (special issue in honor of M. Artin's 70th birthday), 
   vol. 198 (2005), 623-653.
   pdf file
   pdf file of 2nd edition (2009) for semi-free groups

Correction and addendum to "Embedding problems with local conditions",
   Israel Journal of Mathematics, vol. 162 (2007), 373-379.  
   pdf file   
Oort groups and lifting problems (with T. Chinburg and R. Guralnick).
   Compositio Mathematica, vol. 114 (2008), 849-866. 
   pdf file 

On function fields with free absolute Galois groups, Crelle's Journal, 
   vol. 632 (2009), 85-103.  DOI: 10.1515/CRELLE.2009.051.
   pdf file
Applications of patching to quadratic forms and central simple algebras
   (with J. Hartmann and D. Krashen),  Inventiones Mathematicae, 
   vol. 178 (2009), 231-263.  DOI 10.1007/s00222-009-0195-5.  
   The original on-line publication is available at www.springerlink.com.
   pdf file of the preprint

Patching over fields (with J. Hartmann), Israel Journal of Mathematics,
   vol. 176 (2010), 61-107.  DOI 10.1007/s11856-010-0021-1.
   Published on-line June, 2010 at www.springerlink.com. 
   pdf file of the preprint

Permanence criteria for semi-free profinite groups (with L. Bary-Soroker 
   and D. Haran).  Mathematische Annalen, vol. 348, no. 3 (2010), 
   539-563.  DOI 10.1007/s00208-010-0484-8. Published on-line  
   Feb. 2010, at www.springerlink.com.
   pdf file of the preprint

More recent papers.

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