UC Research Profile - University of Canterbury - New Zealand

Dr Brendan Creutz

Contact

Department: Mathematics and Statistics

Email: brendan.creutz@canterbury.ac.nz

Direct Dial: +64 3 3692471

Office: Jack Erskine 612

Languages: English, German

Research / Creative works

Fields of Research

Number Theory
Algebraic Geometry
Computational Algebra

Researcher Summary

Research interests are number theory and algebraic geometry.

Subject Area: Disciplines

Mathematics: Pure Mathematics

Resources

Personal page

Research/Scholarly/Creative Works

Journal Articles

Creutz B. and Viray B. (2022) Quadratic points on intersections of two quadrics. Algebra and Number Theory.

Creutz B. and Voloch JF. (2022) The Brauer-Manin obstruction for constant curves over global function fields. Annales de l'Institut Fourier 72(1): 43-58. http://dx.doi.org/10.5802/aif.3473.

Creutz B. (2020) Generalized Jacobians and explicit descents. Mathematics of Computation 89: 1365-1394. http://dx.doi.org/10.1090/mcom/3491.

Creutz BM. (2020) There are no transcendental Brauer-Manin obstructions on abelian varieties. International Mathematics Research Notices 2020(9): 2684-2697. http://dx.doi.org/10.1093/imrn/rny098.

Creutz B., Ho D. and Steinke GF. (2019) Three-dimensional connected groups of automorphisms of toroidal circle planes. Advances in Geometry http://dx.doi.org/10.1515/advgeom-2019-0031.

Creutz B. (2018) Improved rank bounds from 2-descent on hyperelliptic Jacobians. International Journal of Number Theory 14(6): 1709-1713. http://dx.doi.org/10.1142/S179304211850104X.

Creutz B., Ho D. and Steinke GF. (2018) On automorphism groups of toroidal circle planes. Journal of Geometry 109(1) http://dx.doi.org/10.1007/s00022-018-0420-8.

Creutz B., Viray B. and Skorobogatov AN. (2018) Degree and the brauer–Manin obstruction. Algebra and Number Theory 12(10): 2445-2470. http://dx.doi.org/10.2140/ant.2018.12.2445.

Creutz B., Viray B. and Voloch JF. (2018) The d-primary Brauer–Manin obstruction for curves. Research in Number Theory 4(2) http://dx.doi.org/10.1007/s40993-018-0120-3.

Creutz B. (2017) Zero-cycles of degree one on Skorobogatov's bielliptic surface. Journal of Number Theory 178: 1-4. http://dx.doi.org/10.1016/j.jnt.2017.02.007.

Creutz BM. and Voloch JF. (2017) Local-global principles for Weil-Châtelet divisibility in positive characteristic. Mathematical Proceedings of the Cambridge Philosophical Society 163(2): 357-367. http://dx.doi.org/10.1017/S0305004117000032.

Creutz B. (2016) On the local-global principle for divisibility in the cohomology of elliptic curves. Mathematical Research Letters 23(2): 377-387. http://dx.doi.org/10.4310/MRL.2016.v23.n2.a4.

Creutz B. (2016) Relative Brauer groups of torsors of period two. Journal of Algebra 459: 109-132. http://dx.doi.org/10.1016/j.jalgebra.2016.03.034.

Creutz BM. (2016) Most binary forms come from a pencil of quadrics. Proceedings of the American Mathematical Society Series B 3: 18-27. http://dx.doi.org/10.1090/bproc/24.

Creutz B. and Viray B. (2015) On Brauer groups of double covers of ruled surfaces. Mathematische Annalen 362(3-4): 1169-1200. http://dx.doi.org/10.1007/s00208-014-1153-0.

Creutz B. and Viray B. (2015) Two torsion in the Brauer group of a hyperelliptic curve. Manuscripta Mathematica 147(1): 139-167. http://dx.doi.org/10.1007/s00229-014-0721-7.

Creutz BM. (2014) Second p-descents on elliptic curves. Mathematics of Computation 83(285): 365-409. http://dx.doi.org/10.1090/S0025-5718-2013-02713-5.

Creutz B. (2013) Locally trivial torsors that are not Weil-Châtelet divisible. Bulletin of the London Mathematical Society 45(5): 935-942. http://dx.doi.org/10.1112/blms/bdt019.

Creutz B. (2012) A Grunwald-Wang type theorem for abelain varieties. Acta Arithmetica 154: 353-370. http://dx.doi.org/10.4064/aa154-4-2.

Creutz B. and Miller RL. (2012) Second isogeny descents and the Birch and Swinnerton-Dyer conjectural formula. Journal of Algebra 372: 673-701. http://dx.doi.org/10.1016/j.jalgebra.2012.09.029.

Creutz B. (2011) Potential Sha for abelian varieties. Journal of Number Theory 131: 2162-2174. http://dx.doi.org/10.1016/j.jnt.2011.05.013.

Conference Contributions - Published

Creutz B. (2013) Explicit descent in the Picard group of a cyclic cover of the projective line. In Proceedings of the Tenth Algorithmic Number Theory Symposium: 295-315. http://dx.doi.org/10.2140/obs.2013.1-1.

Chapters

Creutz B. and Voloch JF. (2021) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanoes. In Shaska T; Moshe J (Ed.), Abelian varieties and number theory: 41-50.American Mathematical Society.

Additional Publications

Creutz B. (2010) Explicit second p-descent on elliptic curves. Bremen, Germany. Jacobs University Bremen.