Overview

Research Interests

Algebraic number theory and related topics, including: the equivariant Tamagawa number conjecture (ETNC), Iwasawa theory, Galois module theory, computational number theory, noncommutative Fitting invariants, and integral representation theory.

Papers

Click here for my Google Scholar profile or here for a list of my papers on the arXiv. Note that the publications tab to the right links to an automatically generated page which does not include preprints, etc. See my personal website for a more complete list.

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Publications

_{Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.}

| 2023 | 2020 | 2018 | 2015 | 2013 | 2012 | 2011 | 2009 | 2008 | 2006 |

2023

• Johnston H, Torzewski A. (2023) On the existence of free sublattices of bounded index and arithmetic applications. [PDF]
• Ferri F, Johnston H. (2023) Applications of representation theory and of explicit units to Leopoldt's conjecture. [PDF]

2020

• Bartel A, Johnston H, Jr HWL. (2020) Arakelov class groups of random number fields. [PDF]
• Johnston H, Nickel A. (2020) An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications. [PDF]

2018

• Johnston H, Nickel A. (2018) On the non-abelian Brumer–Stark conjecture and the equivariant Iwasawa main conjecture, Mathematische Zeitschrift, volume 292, no. 3-4, pages 1233-1267, DOI:10.1007/s00209-018-2152-8. [PDF]
• Johnston H, Nickel A. (2018) Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture, American Journal of Mathematics, volume 140, no. 1, pages 245-276, DOI:10.1353/ajm.2018.0005.

2015

• Johnston HLA, Nickel A. (2015) On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results, Transactions of the American Mathematical Society, volume 368, pages 6539-6574, DOI:10.1090/tran/6453. [PDF]
• Johnston H. (2015) Explicit integral Galois module structure of weakly ramified extensions of local fields, Proceedings of the American Mathematical Society, volume 143, no. 12, pages 5059-5071, DOI:10.1090/proc/12634. [PDF]

2013

• Johnston H, Nickel A. (2013) Noncommutative Fitting invariants and improved annihilation results, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, volume 88, pages 137-160, DOI:10.1112/jlms/jdt009. [PDF]

2012

• Greither C, Johnston H. (2012) NON-EXISTENCE AND SPLITTING THEOREMS FOR NORMAL INTEGRAL BASES, ANNALES DE L INSTITUT FOURIER, volume 62, no. 1, pages 417-437, DOI:10.5802/aif.2709. [PDF]

2011

• Bley W, Johnston H. (2011) Computing generators of free modules over orders in group algebras II, MATHEMATICS OF COMPUTATION, volume 80, no. 276, pages 2411-2434, DOI:10.1090/S0025-5718-2011-02488-9. [PDF]
• Burns D, Johnston H. (2011) A non-abelian Stickelberger theorem, Compositio Mathematica, volume 147, no. 1, pages 35-55, DOI:10.1112/S0010437X10004859.
• Byott NP, Carter JE, Greither C, Johnston H. (2011) On the restricted Hilbert-Speiser and Leopoldt properties, Illinois Journal of Mathematics, volume 55, no. 2, pages 623-639.

2009

• Greither C, Johnston H. (2009) On totally real Hilbert-Speiser fields of type C_p, ACTA ARITHMETICA, volume 138, no. 4, pages 329-336, DOI:10.4064/aa138-4-3. [PDF]
• Greither C, Johnston H. (2009) Capitulation for locally free class groups of orders of group algebras over number fields, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, volume 41, pages 541-548, DOI:10.1112/blms/bdp030. [PDF]

2008

• Bley W, Johnston H. (2008) Computing generators of free modules over orders in group algebras, JOURNAL OF ALGEBRA, volume 320, no. 2, pages 836-852, DOI:10.1016/j.jalgebra.2008.01.042. [PDF]
• Johnston H. (2008) Relative Galois module structure of rings of integers of absolutely abelian number fields, Journal fur die Reine und Angewandte Mathematik, no. 620, pages 85-103, DOI:10.1515/CRELLE.2008.050.

2006

• Johnston H. (2006) On the trace map between absolutely abelian number fields of equal conductor, Acta Arithmetica, volume 122, no. 1, pages 63-74, DOI:10.4064/aa122-1-7.

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