Research Papers

[1] On the Riemann-Roch theorem, Math. Colloq. Univ. Cape Town, 13 (1984), 9 – 27.

[2] On the immediate extensions of a valued field, Quaestiones Mathematicae, 9 (1986), 227 – 244.

[3] Immediate extensions of valuation rings, Arch. Math. 53 (1989) 146 – 150.

[4] On the small and essential ideals in certain classes of rings, J. Australian Math. Soc 46 (1989), 262 – 271. Jointly with L. van Wyk.

[5] On the Riemann-Roch theorem for orders in the ring of valuation vectors of a function field, Manuscripta Math. 60 (1988), 259 – 276.

[6] On the embedding of ideals in some one-dimensional local rings, Arch. Math. 50 (1988) 125 – 127. Jointly with E. Jespers.

[7] Functional equations for zeta functions of non-Gorenstein orders in global fields, Manuscripta Math. 64 (1989), 485 – 502.

[8] On valued function fields I, Manuscripta Math. 65 (1989), 357 – 376. Jointly with M. Matignon and F. Pop.

[9] On valued function fields II, Regular functions and elements with the uniqueness property, J. reine angew. Math. 412 (1990), 128 – 149.

Jointly with M. Matignon and F. Pop.

[10] Recent results in the theory of constant reductions, S´eminaire de Th´eorie des Nombres, Bordeaux 3 (1991), 275 – 310.

[11] On valued function fields III, Reductions of algebraic curves, J. reine angew. Math. 432 (1992), 117 – 133. Jointly with M. Matignon and F. Pop.

[12] On the Local Skolem Property, J. reine angew. Math. 458 (1995), 183 – 199. Jointly with M. Matignon and F. Pop.

[13] On Rumely’s Local-Global Principle, Jb. d. Dt. Math.-Verein 97 (1995), 43 – 74. Jointly with P. Roquette and F. Pop.

[14] On the relative genus inequality for curves over valuation rings, J. of Algebra 181 (1996), 836 – 856.

[15] On curves over valuation rings and morphisms to P1, J. of Number Theory 59 (1996), 262 – 290.

[16] Contributions to the Arithmetic of Fields, Notices of the SAMS, 29 (1997), 45 – 60.

[17] Geometric families of Constant Reductions and the Skolem Property, Trans. A.M.S., Vol 350 no. 4, (April 1998), 1379 – 1393.

[18] Liftings of Galois Covers of Smooth Curves, Compositio Math., 113 no. 3 (1998), 239 – 274. Jointly with M. Matignon.

[19] Editorial errata: ‘Liftings of Galois covers of smooth curves Compositio Math. 113 (1998), no. 3, 237 – 272 by B. Green and M. Matignon. Compositio Math.116, no. 2 (1999), 239.

[20] Order p automorphisms of the open disc of a p-adic field, J. of the Amer. Math. Soc., Vol 12 no.1 (1999), 269 – 303. Jointly with M. Matignon.

[21] Deformations of curves and Lubin-Tate formal groups, Israel Journal of Mathematics, 139 (2004), 139 – 148.

Proceedings and other Collections

[22] Algebraic Diophantine Equations, Rumely’s Local-Global Principle, The Encyclopaedia of Mathematics, Supplement I, ISBN 0-7923-4709-9, 43 – 45. Editor: Hazewinkel, Kluwer Academic Publishers, Dordrecht.

[23] Number Theory: Selected Milestones and New Horizons, University of Stellenbosch Inaugural Lecture Series (August 1999), 1 – 16.

[24] On the moduli space of order pn automorphisms of the p -adic open disc, Proceedings Volume of the Symposium on Algebraic Geometry, Kinosaki, Japan, 24 – 27 October 2000, 168 – 181.

[25] On Rumely’s Local-Global Principle, Jointly with P. Roquette, F, Pop. Republished in The Collected Papers of Peter Roquette, Vol 3, ISBN 088911-868-X, Queen’s University, Kingston, Canada, 2002, 189 – 220.

[26] Automorphisms of formal power series rings over a valuation ring, In Valuation Theory and its Applications II, Fields Institute Communications Volume 33, ISBN 0-8218-3206-9, American Mathematical Society, 2003, 79 – 87.

[27] The African Institute for the Mathematical Sciences, Mitteilungen der Deutschen Mathematiker-Vereinigung Band 15, Heft 2 (2007), 106 – 109.

Manuscripts in preparation

[28] The Hadamard Quotient Theorem in characteristic p and applications, manuscript, 15 pages.

[29] An Introduction to Deuring’s Theory of Constant Reductions, manuscript in preparation jointly with Peter Roquette.

[31] Finite order automorphisms of the p-adic disc, Lecture notes in preparation for World Scientific, following seminar presented at the University of Pennsylvania, 2007.

Please e-mail me if you would like a copy of any of my papers.