Florida Atlantic University

Welcome to T. J. Ford's Homepage

Biographical Sketch

Research Interests

Mathematics Subject Classification 14F22, 16K50, 16H05, 14F20. The Brauer group of a commutative ring, the Brauer group of a variety, Azumaya algebras defined over the function field of a variety, étale cohomology, commutative algebra and algebraic geometry. 

Publications

  1. (with I. D. Palmer, and R. Sanders), Separation of solar and interplanetary diffusion in solar cosmic ray events, J. Geophys. Res., 82 (1977), pp. 4704--4709.
  2. (with F. R. DeMeyer), On units of group rings, J. Pure Appl. Algebra, 16 (1980), pp. 245--248. doi:10.1016/0022-4049(80)90028-6
  3. Every finite abelian group is the Brauer group of a ring, Proc. Amer. Math. Soc., 82 (1981), pp. 315--321. doi:10.1090/S0002-9939-1981-0612710-X
  4. (with F. R. DeMeyer), On the Brauer group of surfaces and subrings of k[x,y], in Brauer Groups in Ring Theory and Algebraic Geometry, vol. 917 of Lecture Notes in Math., 1982, Springer-Verlag, Berlin, pp. 211--221. pdf file.
  5. (with F. R. DeMeyer), On the Brauer group of surfaces, J. Algebra, 86 (1984), pp. 259--271. doi:10.1016/0021-8693(84)90065-6
  6. Hecke actions on Brauer groups, J. Pure Appl. Algebra, 33 (1984), pp. 11--17. doi:10.1016/0022-4049(84)90021-5
  7. (with F. R. DeMeyer), Homomorphisms of progenerator modules, J. Algebra, 113 (1988), pp. 379--398. doi:10.1016/0021-8693(88)90167-6
  8. Homomorphisms of progenerator modules under a change of base ring, Comm. Algebra, 16 (1988), pp. 457--482.
  9. On the Brauer group of a Laurent polynomial ring, J. Pure Appl. Algebra, 51 (1988), pp. 111--117. doi:10.1016/0022-4049(88)90081-3
  10. (with F. R. DeMeyer), Computing the Brauer-Long group of Z/2-dimodule algebras, J. Pure Appl. Algebra, 54 (1988), pp. 197--208. doi:10.1016/0022-4049(88)90030-8
  11. On the Brauer group of k[x1, ..., xn,1/f], J. Algebra, 122 (1989), pp. 410--424. doi:10.1016/0021-8693(89)90226-3
  12. On the Brauer group and the cup product map, in Perspectives in Ring Theory, F. van Oystaeyen and L. Le Bruyn, eds., NATO ASI series, Kluwer Academic Publ., Dordrecht, 1988, pp. 135--145. pdf file
  13. On the Brauer group of a localization, J. Algebra, 147 (1992), pp. 365--378. doi:10.1016/0021-8693(92)90211-4
  14. (with D. Saltman), Division algebras over henselian surfaces, Israel Mathematical Conference Proceedings, 1 (1989), pp. 320--336. pdf file
  15. Division algebras over nonlocal henselian surfaces, Pacific J. Math., 147 (1991), pp. 301--310.
  16. (with F. R. DeMeyer, and H. P. Miranda), Rational singularities and the Brauer group, J. Algebra, 162 (1993), pp. 287--294. doi:10.1006/jabr.1993.1253
  17. On the Brauer group and quotient singularities, Illinois J. Math., 35 (1991), pp. 496--498.
  18. (with F. R. DeMeyer), On the Brauer group of toric varieties, Trans. Amer. Math. Soc., 335 (1993) pp. 559--577. doi:10.1090/S0002-9947-1993-1085941-8
  19. (with F. R. DeMeyer), Nontrivial, locally trivial Azumaya algebras, in Azumaya Algebras, Actions, and Modules, D. Haile and J. Osterburg, eds., vol. 124 of Contemporary Mathematics, AMS, 1992, pp. 39--49. Corrections to "Nontrivial, locally trivial Azumaya algebras", by DeMeyer and Ford, pdf file
  20. (with J. Blass, and P. Blass), On a remark of Grothendieck, Comm. Algebra, 18 (1990), pp. 3685--3687. pdf file DOI:10.1080/00927879008824101
  21. On the Brauer group of a desingularization of a normal surface, Comm. Algebra, 20 (1992), pp. 3785--3791. DOI:10.1080/00927879208824543
  22. The Brauer group and ramified double covers of surfaces, Comm. Algebra, 20 (1992), pp. 3793--3803. DOI:10.1080/00927879208824544
  23. Products of symbol algebras that ramify only on a nonsingular plane elliptic curve, The Ulam Quarterly, 1 (1992), pp. 12--16. PostScript file
  24. (with F. R. DeMeyer, and H. P. Miranda), The cohomological Brauer group of toric varieties, J. of Alg. Geom., 2 (1993) pp. 137--154.
  25. Examples of locally trivial Azumaya algebras, K-theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras (Santa Barbara, CA, 1992), vol. 58 of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, 1995, pp. 197--216. pdf file
  26. Topological invariants of a fan associated to a toric variety, Comm. Algebra, 23 (1995), pp. 4031--4045. pdf file DOI:10.1080/00927879508825447
  27. Division algebras and quadratic reciprocity, pdf file
  28. (with J. Brewer, L. Klingler and W. Schmale) When does the ring K[Y] have the coefficient assignment property?, J. Pure Appl. Algebra, 112 (1996), pp. 239--246. doi:10.1016/0022-4049(95)00142-5
  29. The toroidal embedding arising from an irrational fan, Resultate Math. 35 (1999), pp. 44--69. pdf file.
  30. The Brauer group of a curve over a strictly local discrete valuation ring, Israel J. Math. 96 (1996), pp. 259--266. pdf file.
  31. Division algebras that ramify only along a singular plane cubic curve, New York J. Math. 1 (1995) pp. 178--183.
  32. The Brauer group of an affine cone, J. Pure Appl. Algebra, 155 (2001), pp. 29--40. doi:10.1016/S0022-4049(99)00074-2
  33. (with R. Stimets), The Picard group of a general toric variety of dimension three, Comm. Algebra, 30 (2002), pp. 5771-­-5779. DOI:10.1081/AGB-120016010
  34. The Brauer Group of a Toric Variety associated to a Finite Distributive Lattice, J. Pure Appl. Algebra, 159 (2001), pp. 75-­-82. doi:10.1016/S0022-4049(00)00124-9
  35. Division algebras that ramify only on a plane quartic curve with simply connected components, Algebr. Represent. Theory, 6 (2003), pp. 501-­-514. doi:10.1023/B:ALGE.0000006494.31777.00
  36. Division algebras that ramify only on a plane nodal cubic curve plus a line, J. Pure Appl. Algebra, 188 (2004), pp. 117-­-126. doi:10.1016/j.jpaa.2003.10.015
  37. Division algebras that ramify only on the zeros of an elementary symmetric polynomial , Int. Electron. J. Algebra., 2 (2007), pp. 189-­-207. pdf file.
  38. The relative Brauer group of a cyclic cover of affine space, J. Pure Appl. Algebra, 215 (2011), pp. 847-­-865. doi:10.1016/j.jpaa.2010.06.030
  39. The relative Brauer group of an affine double plane, Comm. Algebra, 41 (2013), pp. 3277-­-3298. doi:10.1080/00927872.2012.682677
  40. (with D. N. Bulj and D. M. Harmon), Generically trivial Azumaya algebras on a rational surface with a non rational singularity, Comm. Algebra, 41 (2013), pp. 4333-­-4338. doi:10.1080/00927872.2012.695837
  41. The Group of Units on an Affine Variety, Journal of Algebra and its Applications, 13 (2014), (27 pages). DOI: 10.1142/S0219498814500650.
  42. The Brauer group of an affine double plane associated to a hyperelliptic curve, Comm. Algebra, 45 (2017), pp. 1416-­-1442. DOI: 10.1080/00927872.2016.1175608.
  43. (with D. M. Harmon), The Relative Brauer Group and Generalized Cross Products for a Cyclic Covering of Affine Space, J. Pure Appl. Algebra, 218 (2014), pp. 721-­-730. doi:10.1016/j.jpaa.2013.08.010
  44. (with D. M. Harmon), The Brauer Group of an Affine Rational Surface with a Non-rational Singularity, J. Algebra, 388 (2013), pp. 107-­-140. doi:10.1016/j.jalgebra.2013.04.022
  45. The Relative Brauer Group and Generalized Cyclic Crossed Products for a Ramified Covering, J. Algebra, 450 (2016), pp. 1-­-58. doi:10.1016/j.jalgebra.2015.10.013
  46. Separable Algebras, Graduate Studies in Mathematics, Vol. 183, The American Mathematical Society, Providence, RI, 2017. Link to the AMS Bookstore. Errata. A proof of Theorem 14.2.1 (A theorem of Bass).
  47. A Family of Nonnormal Double Planes Associated to Hyperelliptic Curves, in Algebraic Curves and Applications, vol. 724 of Contemporary Mathematics, AMS, 2019, pp. 45-­-54. doi:10.1090/conm/724/14584
  48. Commutative Algebra, AMS Open Math Notes, Reference # OMN:202409.111443, 529 pages, 2024 An algebra book containing an introduction to the theory of commutative algebra. Freely available as a pdf file at AMS Open Math Notes. The latest version is here: pdf file.
  49. Investigating Algebraic Surfaces Associated to Elliptic Curves, a poster for the Department of Mathematical Sciences, Charles E. Schmidt College of Science, Florida Atlantic University pdf file.
  50. Introduction to Abstract Algebra. AMS Open Math Notes, Reference # OMN:202006.110827, 350 pages, 2024. An algebra book containing an introduction to groups, rings, linear algebra, and fields. Based on my notes for the two semester course: Introduction to Abstract Algebra. Freely available as a pdf file at AMS Open Math Notes. The latest version is here: pdf file.
  51. Abstract Algebra, pre-preprint. An algebra book. The first half consists of an introduction to group theory, ring theory, linear algebra, fields, modules. The second half contains additional results on commutative algebra, ring theory, and an introduction to homological algebra. Under constant revision, the latest version is here: pdf file.
  52. Division Algebras and the Picard Number of a Ramified Cyclic Covering, preprint, pdf file.

DeMeyer, Harrison and Ford

Photograph of Ford, Frank DeMeyer and David Harrison

This photograph was taken in June of 1994 on the campus of The University of Oregon. The three mathematicians visible in the picture are (from left to right) Timothy J. Ford, Frank R. DeMeyer and David K. Harrison. DeMeyer was my Ph.D. thesis advisor and Harrison was DeMeyer's.
Timothy J. Ford