Nigel Byott's List of Publications

Preprints and papers to appear:

• (with C. Greither and B. Sodaigui) Classes realisables d'extensions non abeliennes, submitted (version of October 2004).

Published research papers:

• (with G. Griffith Elder), New ramification breaks and additive Galois structure, Journal de Théorie des Nombres de Bordeaux 17 (2005), 87-107.

• (with B. Sodaigui), Realizable Galois module classes for tetrahedral extensions, Compositio Mathematica 141 (2005), 573-582.

• (with B. Sodaigui), Galois module structure for dihedral extensions of degree 8: realizable classes over the group ring, Journal of Number Theory 112 (2005), 1-19.

• Monogenic Hopf orders and associated orders of valuation rings, Journal of Algebra 275 (2004), 575-599.

• Hopf-Galois structures on Galois field extensions of degree $pq$, Journal of Pure & Applied Algebra 188 (2004), 45-57.

• Hopf-Galois structures on field extensions with simple Galois groups, Bulletin of the London Mathematical Society 36 (2004), 23-29.

• (with G Griffith Elder), Biquadratic extensions with one break, Canadian Mathematical Bulletin 45 (2002) 168-179.

• Integral Hopf-Galois structures on degree p^2 extensions of p-adic fields, Journal of Algebra 248 (2002) 334-365.

• Galois module theory and Kummer theory for Lubin-Tate formal groups, pp 55-67 in "Algebraic Number Theory and Diophantine Analysis" (F Halter-Koch, R Tichy, eds), (Proceedings of Conference in Graz, 1998), Walter de Gruyter, 2000.

• Picard invariants of Galois algebras over dual Larson Hopf Orders, Proceedings of the London Mathematical Society (3) 80 (2000), 1-30.

• Integral Galois module structure of some Lubin-Tate extensions, Journal of Number Theory 77 (1999), 252-273.

• (with Robin J Chapman), Power sums of finite subspaces of a field, Finite Fields and their Applications 5 (1999), 254-265.

• Tame realisable classes over Hopf orders, Journal of Algebra 201 (1998), 284-316.

• Associated orders of certain extensions arising from Lubin-Tate formal groups, Journal de Theorie des Nombres de Bordeaux 9 (1997), 449-462.

• Galois structure of ideals in wildly ramified abelian $p$-extensions of a $p$-adic field, and some applications, Journal de Theorie des Nombres de Bordeaux 9 (1997), 201-219.

• Two constructions with Galois objects, Communications in Algebra 25 (1997), 3513-3520.

• Uniqueness of Hopf Galois structures for separable field extensions, Communications in Algebra 24 (1996) 3217-3228. Corrigendum, ibid., 3705.

• (with G.Lettl): Relative Galois module structure of abelian fields, Journal de Theorie des Nombres de Bordeaux 8 (1996), 125-141.

• Tame and Galois extensions with respect to Hopf orders, Mathematische Zeitschrift 220 (1995), 495-522.

• Hopf orders and a generalisation of a theorem of L.R.McCulloh, Journal of Algebra 177 (1995), 409-433.

• Local Galois module structure and Hopf orders}, pp. 249-255 in Symposia Gaussiana, Conf. A (eds. M.Behara, R.Fritsch, R.G.Lintz) Walter de Gruyter & Co, 1995

• Cleft Extensions of Hopf Algebras, II, Proceedings of the London Mathematical Society (3) 67 (1993), 277-304.

• Cleft Extensions of Hopf Algebras, Journal of Algebra 157 (1993), 405-429.

• Toroidal block decompositions of Hopf orders in group algebras, Proceedings of the London Mathematical Society (3) 65 (1992), 449-473.

• On Galois isomorphisms between ideals in extensions of local fields, Manuscripta Mathematica 73 (1991), 289-311.

• Some self-dual local rings of integers not free over their associated orders, Mathematical Proceedings of the Cambridge Philosophical Society 110 (1991), 5-10. Corrigendum, ibid., 116 (1994), 569.

Other publications:

• Review of "Galois Theories" by F Borceux and G Janelidze, Bulletin of the London Mathematical Society 34 (2002), 376-378.

• M.J.Taylor with contributions by N.P.Byott: Hopf Orders and Galois Module Structure}, (expanded notes of lectures given by the first author, written up by the second), pp. 153-210 in K.W. Roggenkamp, M.J.Taylor, ``Group Rings and Class Groups'', DMV Seminar, Band 18, Birkhauser 1992.

• Ph.Cassou-Nogues, T.Chinburg, A.Frohlich, M.J.Taylor: L-Functions and Galois Modules, (expanded notes of lectures by the 4 main authors, written up by D.Burns and N.P.Byott), pp 75-139 in ``L-Functions and Arithmetic'' (Proceedings of the Durham Symposium, July 1989), LMS Lecture Notes No.\ 153, CUP 1991

• plus more than 60 reviews written for Mathematical Reviews.