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. pdf file 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, 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
More recent papers.
Back to David Harbater's Home Page.