Staff profile

• Algebraic number theory
• Arithmetical number theory

• 2000: 'Networks': 'A member of the Durham node of the European Arithmetic Algebraic Geometry network'

Chapter in book

• Galois groups of local fields, Lie algebras and ramification
  Abrashkin, V. (2015). Galois groups of local fields, Lie algebras and ramification. In L. Dieulefait, G. Faltings, D. Heath-Brown, Y. Manin, B. Moroz, & J.-P. Wintenberger (Eds.), Arithmetic and geometry (1-23). (New ed.). Cambridge University Press. https://doi.org/10.1017/cbo9781316106877.006
• A semi-stable case of the Shafarevich Conjecture
  Abrashkin, V. (2014). A semi-stable case of the Shafarevich Conjecture. In F. Diamond, P. L. Kassaei, & M. Kim (Eds.), Automorphic forms and galois representations (1-31). (New ed.). Cambridge University Press. https://doi.org/10.1017/cbo9781107446335.002

Journal Article

• Galois groups of p-extensions of higher local fields
  Abrashkin, V. (2024). Galois groups of p-extensions of higher local fields. Journal de théorie des nombres de Bordeaux, 36(2), 671-724. https://doi.org/10.5802/jtnb.1293/
• Ramification Filtration and Differential Forms
  Abrashkin, V. (2023). Ramification Filtration and Differential Forms. Izvestiâ Rossijskoj akademii nauk. Seriâ matematičeskaâ Известия Российской академии наук. Серия математическая (Online), 87(3), 5-22. https://doi.org/10.4213/im9322
• Ramification filtration via deformations
  Abrashkin, V. A. (2021). Ramification filtration via deformations. Sbornik: Mathematics, 212(2), Article 135. https://doi.org/10.1070/sm9322
• Groups of automorphisms of local fields of period p and nilpotent class < p, II
  Abrashkin, V. (2017). Groups of automorphisms of local fields of period p and nilpotent class < p, II. International Journal of Mathematics, 28(10), Article 1750066. https://doi.org/10.1142/s0129167x17500665
• Groups of automorphisms of local fields of period p and nilpotent class < p, I
  Abrashkin, V. (2017). Groups of automorphisms of local fields of period p and nilpotent class < p, I. International Journal of Mathematics, 28(06), Article 1750043. https://doi.org/10.1142/s0129167x17500434
• Groups of automorphisms of local fields of period p^M and nilpotent class < p
  Abrashkin, V. (2017). Groups of automorphisms of local fields of period p^M and nilpotent class < p. Annales de l'Institut Fourier, 67(2), 605-635. https://doi.org/10.5802/aif.3093
• Ramification estimate for Fontaine-Laffaille Galois modules
  Abrashkin, V. (2015). Ramification estimate for Fontaine-Laffaille Galois modules. Journal of Algebra, 427, 319-328. https://doi.org/10.1016/j.jalgebra.2014.11.029
• Group schemes of period 2
  Abrashkin, V. (2014). Group schemes of period 2. manuscripta mathematica, 143(3), 317-353. https://doi.org/10.1007/s00229-013-0620-3
• Projective Varieties with Bad Semi-stable Reduction at 3 Only
  Abrashkin, V. (2013). Projective Varieties with Bad Semi-stable Reduction at 3 Only. Documenta Mathematica, 18, 547-619
• The field-of-norms functor and the Hilbert symbol for higher local fields
  Abrashkin, V., & Jenni, R. (2012). The field-of-norms functor and the Hilbert symbol for higher local fields. Journal de théorie des nombres de Bordeaux, 24(1), 1-39. https://doi.org/10.5802/jtnb.786
• Group schemes of period p>2
  Abrashkin, V. (2010). Group schemes of period p>2. Proceedings of the London Mathematical Society, 101(1), 207-259. https://doi.org/10.1112/plms/pdp052
• Modified proof of a local analogue of the Grothendieck Conjecture
  Abrashkin, V. (2010). Modified proof of a local analogue of the Grothendieck Conjecture. Journal de théorie des nombres de Bordeaux, 22(1), 1-50. https://doi.org/10.5802/jtnb.703
• Characteristic p analogue of modules with finite crystalline height
  Abrashkin, V. (2009). Characteristic p analogue of modules with finite crystalline height. Pure and Applied Mathematics Quarterly, 5(1), 469-494. https://doi.org/10.4310/pamq.2009.v5.n1.a14
• An analogue of the field-of-norms functor and of the Grothendieck Conjecture
  Abrashkin, V. (2007). An analogue of the field-of-norms functor and of the Grothendieck Conjecture. Journal of Algebraic Geometry, 16(4), 671-730. https://doi.org/10.1090/s1056-3911-07-00470-5
• A local analogue of the Grothendieck conjecture
  Abrashkin, V. (2000). A local analogue of the Grothendieck conjecture. International Journal of Mathematics, 11(02), 133-175. https://doi.org/10.1142/s0129167x0000009x
• The image of the Galois group for some crystalline representations
  Abrashkin, V. (1999). The image of the Galois group for some crystalline representations. Izvestiya: Mathematics, 63(1), 1-36
• The field of norms functor and the Brueckner-Vostokov formula
  Abrashkin, V. (1997). The field of norms functor and the Brueckner-Vostokov formula. Mathematische Annalen, 308, 5-19
• Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors
  Abrashkin, V. (1997). Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors. Izvestiya: Mathematics, 61(3), 463-515. https://doi.org/10.1070/im1997v061n03abeh000122