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Arithmetic discriminants and horizontal intersections,
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Abhyankar's conjecture on Galois groups over curves, Inventiones Math.,
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Contemporary Mathematics Series, vol. 174, 1994, pp. 35-60.
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Approximating Galois orbits of dessins (with L. Schneps), in "Geometric
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series, vol. 242, Cambridge University Press, 1997, pp.205-230.
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Fields of definition of p-adic covers (with P. Dèbes), Crelle's Journal,
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Patching and thickening problems (with K. Stevenson), J. Alg., vol. 212
(1999), 272-304.
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Embedding problems and adding branch points, in "Aspects of Galois
Theory", London Mathematical Society Lecture Note series, vol. 256,
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Embedding problems with local conditions, Israel Journal of Mathematics,
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pdf file of paper
pdf file of correction/addendum
Valued fields and covers in characteristic p (with M. van der Put,
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Applications", Fields Institute Communications, vol.32,
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in "Algebra, Arithmetic and Geometry with Application" (Abhyankar 70th
birthday conference proceedings, C.Christensen et al., eds.),
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pdf file
Patching and Galois theory. In "Galois Groups and Fundamental Groups"
(L. Schneps, ed.), MSRI Publications series, vol.41,
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Long pdf file of the whole paper;
or two shorter pdf files: part 1 and part 2
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Math. (special issue in honor of M. Artin's 70th birthday),
vol. 198 (2005), 623-653.
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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.
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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.
pdf file
Patching over fields (with J. Hartmann), Israel Journal of Mathematics,
vol. 176 (2010), 61-107. DOI 10.1007/s11856-010-0021-1.
pdf file
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.
pdf file
The local lifting problem for actions of finite groups on curves (with
T. Chinburg and R. Guralnick). Annales scientifiques de l'ENS,
vol. 44, no. 4 (2011), 537-605.
pdf file
Patching subfields of division algebras (with J. Hartmann and D. Krashen).
Transactions of the AMS, vol. 363, no. 6 (2011), 3335-3349.
pdf file
Embedding problems and open subgroups (with K. Stevenson).
Proceedings of the AMS, vol. 139, no. 4 (2011), 1141-1154.
pdf file
Division algebras and patching (with J. Hartmann). Lecture notes for
the 2012 Arizona Winter School. 2012 manuscript. pdf file
Also available at the AWS 2012 website.
Patching in Algebra: Notes from the Luxembourg Winter School,
in "Winter School on Galois Theory Volume II: Luxembourg 2012",
Travaux mathematiques, Volume 23 (2013), 37-86, University of Luxembourg,
ed. by Gabor Wiese, Sara Arias-de-Reyna, and Lior Bary-Soroker.
pdf file
Weierstrass preparation and algebraic invariants (with J. Hartmann
and D. Krashen). Mathematische Annalen, vol. 356, no. 4 (2013),
1405-1424. DOI 10.1007/s00208-012-0888-8.
pdf file
Local-global principles for Galois cohomology (with J. Hartmann
and D. Krashen). Commentarii Mathematici Helvetici,
vol. 89, no. 1 (2014), 215-253. DOI 10.4171/CMH/317.
pdf file
Shreeram Abhyankar (July 22, 1930 - November 2, 2012), S. Mulay and
A. Sathaye, eds. Notices of the AMS, vol. 61, no. 10, Nov. 2014,
1196-1216. D. Harbater portion: 1205-1207. pdf file.
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