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Durham University

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Staff Profile

Victor Abrashkin, PhD Moscow State University

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2H Course Director, Professor, Algebra in the Department of Mathematical Sciences

Contact Victor Abrashkin

Research Groups

Department of Mathematical Sciences

  • Pure Mathematics
  • Pure Mathematics: Algebra & Number Theory

Research Interests

  • Algebraic number theory
  • Arithmetical number theory

Publications

Chapter in book

  • Abrashkin, Victor (2015). Galois groups of local fields, Lie algebras and ramification. In Arithmetic and Geometry. Dieulefait, L., Faltings, G., Heath-Brown, D.R., Manin, Y.I., Moroz, B.Z. & Wintenberger, J.-P. Cambridge: Cambridge University Press. 420: 1-23.
  • Abrashkin, Victor (2014). A semi-stable case of the Shafarevich Conjecture. In Automorphic forms and galois representations. Diamond, Fred, Kassaei, Payman L. & Kim, Minhyong Cambridge: Cambridge University Press. 1: 1-31.

Journal Article

  • Abrashkin, Viktor Aleksandrovich (2021). Ramification filtration and deformations. Sbornik: Mathematics 212(2).
  • Abrashkin, Victor (2017). Groups of automorphisms of local fields of period p and nilpotent class < p, I. International Journal of Mathematics 28(06): 1750043.
  • Abrashkin, Victor (2017). Groups of automorphisms of local fields of period p and nilpotent class < p, II. International Journal of Mathematics 28(10): 1750066.
  • Abrashkin, Victor (2017). Groups of automorphisms of local fields of period p^M and nilpotent class < p. Annales de l'Institut Fourier 67(2): 605-635.
  • Abrashkin, V. (2015). Ramification estimate for Fontaine-Laffaille Galois modules. Journal of Algebra 427: 319-328.
  • Abrashkin, Victor (2014). Group schemes of period 2. Manuscripta Mathematica 143(3): 317-353.
  • Abrashkin, Victor (2013). Projective Varieties with Bad Semi-stable Reduction at 3 Only. Documenta Mathematica 18: 21, 547-619.
  • Abrashkin, Victor & Jenni, Ruth (2012). The field-of-norms functor and the Hilbert symbol for higher local fields. Journal Theorie des Nombres de Bordeaux 24(1): 1-39.
  • Abrashkin, Victor (2010). Group schemes of period p>2. Proceedings of London Mathematical Society 101(1): 207-259.
  • Abrashkin, Victor (2010). Modified proof of a local analogue of the Grothendieck Conjecture. Journal Theorie des Nombres de Bordeaux 22(1): 1-50.
  • Abrashkin, Victor (2009). Characteristic p analogue of modules with finite crystalline height. Pure and Applied Mathematics Quarterly 5(1): 469-494.
  • Abrashkin, Victor (2007). An analogue of the field-of-norms functor and of the Grothendieck Conjecture. Journal of Algebraic Geometry 16(4): 671-730.
  • Abrashkin, V. (2000). A local analogue of the Grothendieck conjecture. International journal of mathematics 11(02): 133-175.
  • Abrashkin, V. (1999). The image of the Galois group for some crystalline representations. Izvestiya: Mathematics 63(1): 1-36.
  • Abrashkin, V. (1997). Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors. Izvestiya: Mathematics 61(3): 463-515.
  • Abrashkin, V. (1997). The field of norms functor and the Brueckner-Vostokov formula. Mathematische Annalen 308: 5-19.