Dr Bernhard Koeck

Reader in Pure Mathematics

Dr Bernhard Koeck is a Reader within Mathematical Sciences at the University of Southampton.

Background

PhD Regensburg, Habilitation Karlsruhe, Heisenberg Fellow

Research

Responsibilities

Publications

Teaching

Contact

Research interests

Dr Koeck is an algebraist with research interests in Algebraic Geometry, Algebraic K-Theory, Algebraic Number Theory and Homological Algebra. A common theme in Koeck's research form group actions on spaces in Algeba, Geometry and Number Theory. More specifically he has worked in (equivariant) Riemann-Roch theory, higher K-theory (of group rings), Galois module theory, Belyi theory and simplicial homological algebra.

Research group

Pure Mathematics

Affiliate research group

Algebraic Geometry

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Articles

Koeck, B., & Tait, J. (2018). On the de-Rham cohomology of hyperelliptic curves. Research in Number Theory, 4(2), 1-17. [19]. DOI: 10.1007/s40993-018-0111-4
Harris, T., Koeck, B., & Taelman, L. (2017). Exterior power operations on higher K-groups via binary complexes. Annals of K-Theory, 2(3), 409-450. DOI: 10.2140/akt.2017.2.409
Fischbacher-Weitz, H. B., & Koeck, B. (2017). Galois-module theory for wildly ramified covers of curves over finite fields: [With an appendix by Bernhard Koeck and Adriano Marmora: Integrality of epsilon representations of wildly ramified Galois covers]. arXiv.
Koeck, B., & Tait, J. (2015). Faithfulness of actions on Riemann-Roch spaces. Canadian Journal of Mathematics, 67(4), 848-869. DOI: 10.4153/CJM-2014-015-2
Pink, R., Rössler, D., & Koeck, B. (2012). On the Adams-Riemann-Roch theorem in positive characteristic. [With an appendix by B. Koeck: Another formula for the Bott element]. Mathematische Zeitschrift, 270(3-4), 1067-1076.
Koeck, B., & Kontogeorgis, A. (2012). Quadratic differentials and equivariant deformation theory of curves. Annales de l'Institut Fourier, 62(3), 1-29.
Koeck, B., & Lau, E. (2010). A note on Belyi's theorem for Klein surfaces. Quarterly Journal of Mathematics, 61(1), 103-107. DOI: 10.1093/qmath/han034
Satkurunath, R., & Koeck, B. (2010). An algorithmic approach to Dold-Puppe complexes. Homology, Homotopy and Applications, 12(1), 301-326.
Fischbacher-Weitz, H. B., & Koeck, B. (2009). Equivariant Riemann-Roch theorems for curves over perfect fields. Manuscripta Mathematica, 128(1), 89-105. DOI: 10.1007/s00229-008-0218-3
Koeck, B. (2009). Faithful action on the space of global differentials of an algebraic curve. Pre-print, 7pp.
Koeck, B., & Satkurunath, R. (2009). On the derived functors of the third symmetric-power functor. Tbilisi Mathematical Journal, 2, 19-39.
Koeck, B., & Singerman, D. (2007). Real Belyi theory. Quarterly Journal of Mathematics, 58(4), 463-478. DOI: 10.1093/qmath/ham017
Koeck, B. (2005). Computing the equivariant Euler characteristic of Zariski and étale sheaves on curves. Homology, Homotopy and Applications, 7(3), 83-98.
Koeck, B. (2004). Belyi's theorem revisited. Beiträge zur Algebra und Geometrie, 45(1), 253-265.
Koeck, B. (2004). Galois structure of Zariski cohomology for weakly ramified covers of curves. American Journal of Mathematics, 126(5), 1085-1107. DOI: 10.1353/ajm.2004.0037
Baumgartl, T., & Koeck, B. (2004). Modelling volume change and mechanical properties with hydraulic models. SSSAJ Soil Science Society of America Journal, 68(1), 57-65. DOI: 10.2136/sssaj2004.5700
Burns, D., Koeck, B., & Snaith, V. (2004). Refined and l-adic Euler characteristics of nearly perfect complexes. Journal of Algebra, 272(1), 247-272. DOI: 10.1016/j.jalgebra.2003.09.009
Koeck, B. (2001). Computing the homology of Koszul complexes. Transactions of the American Mathematical Society, 353(8), 3115-3147. DOI: 10.1090/S0002-9947-01-02723-4
Koeck, B. (2000). Riemann-Roch for tensor powers. Mathematische Zeitschrift, 233(4), 755-801. DOI: 10.1007/s002090050497
Koeck, B. (2000). Symmetric powers of Galois modules on Dedekind schemes. Compositio Mathematica, 124(2), 195-217. DOI: 10.1023/A:1026579331113
Koeck, B. (1999). Operations on locally free classgroups. Mathematische Annalen, 314(4), 667-702. DOI: 10.1007/s002080050312
Koeck, B. (1998). The Grothendieck-Riemann-Roch theorem for group scheme actions. Annales Scientifiques de l'Ecole Normale Supérieure, 31(3), 415-458. DOI: 10.1016/S0012-9593(98)80140-7

GENG0001 Mathematics A

MATH3078 Further Number Theory

Dr Bernhard Koeck
Building 54 Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ

Room Number: 54/7015

Facsimile: (023) 8059 5147

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