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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, pp.360-361. 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

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