Henri Johnston

Contact Information St John's College Cambridge CB2 1TP United Kingdom Phone (college): +44 1223 766724 Phone (dept): +44 1223 765901 Office (college): B8 New Court Office (dept): C2.01 Fax : +44 1223 337720 Email: [my first initial] dot [my last name] at dpmms.cam.ac.uk About me I am fellow and college lecturer in pure mathematics at St. John's College, Cambridge. I was previously stipendiary lecturer in pure maths at St. Hugh's College, Oxford. In August 2007, I finished as a graduate student in the mathematics department at Cornell University where my supervisor was Ravi Ramakrishna. For the 2006-07 academic year, I visited Cornelius Greither at Universität der Bundeswehr München, Germany. I am originally from Jersey in the Channel Islands. Research Interests Algebraic number theory, including: Galois module structure, Stark's conjectures, computational number theory. Algebra and respresentation theory with applications to algebraic number theory, including noncommutative Fitting invariants.

Graduate Course

• Galois Modules

Papers

• Trivial integral Galois module structure of weakly ramified extensions of p-adic fields, preprint (under revision). [arXiv]
• (with Andreas Nickel) Noncommutative Fitting invariants and improved annihilation results, submitted. [arXiv]
• (with Werner Bley) Computing generators of free modules over orders in group algebras II, Math. Comp. 80 (2011), 2411-2434. [Journal] [arXiv] [MR] [ZB]
• (with Nigel P. Byott, James E. Carter and Cornelius Greither) On the restricted Hilbert-Speiser and Leopoldt properties, to appear in Illinois Journal of Mathematics. [arXiv]
• (with David Burns) A non-abelian Stickelberger theorem, Compositio Math. 147 (2011), 35-55. [Journal] [arXiv] [MR] [ZB]
• (with Cornelius Greither) On totally real Hilbert-Speiser fields of type C_p, Acta Arith. 138 (2009), no. 4, 329-336. [Journal] [arXiv] [MR] [ZB]
• (with Cornelius Greither) Non-existence and splitting theorems for normal integral bases, to appear in Annales de l'Institut Fourier. [arXiv]
• (with Werner Bley) Computing generators of free modules over orders in group algebras, J. Algebra 320 (2008), no. 2, 836-852. [Journal] [arXiv] [MR] [ZB]
• (with Cornelius Greither) Capitulation for locally free class groups of orders of group algebras over number fields, Bull. London Math. Soc. 41 (2009), 541-548. [Journal] [arXiv] [MR] [ZB]
• Relative Galois module structure of rings of integers of absolutely Abelian number fields, J. reine angew. Math. 620 (2008), 85-103. [Journal] [arXiv] [MR] [ZB]
• On the trace map between absolutely Abelian number fields of equal conductor, Acta Arith. 122 (2006), no.1, 63-74. [Journal] [arXiv] [MR] [ZB]

Maths Books and Notes

• Online notes of interest to number theorists (and others)
• MathOnline
• Free mathemamatics e-books
• Springerlink (lots of Springer books and articles available online if your university has a subscription)
• Cambridge books online (lots of CUP books online if your university has a subscription)
• MathSciNet (often the easiest way to find electronic versions of maths books online if your university has a subscription; once you have found the review, click on the "book" link).
• Best book price (UK book price comparison website)

Maths Links

• MathOverflow
• Detexify (draw a symbol to get the corresponding latex command)
• Number Theory Web (British mirror)
• Conferences in arithmetic geometry