title: Honda formal group in unramified p-extension of local field as Galois module
metadata.name: dc.contributor.author
metadata.value: Hakobyan, Tigran L.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vostokov, Sergei V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:18:19Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:18:19Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Hakobyan T. L., Vostokov S.V. Honda formal group in unramified p-extension of local field as Galois module. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 541–548.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15123
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let p be a rational prime. Let K/Qp, L/K, and M/L be finite extensions of local fields, let
  M/L be a Galois extension with Galois group G, and let F be a one-dimensional formal
  group law over the ring OK. We denote by F(mM) the abelian group whose underlying
  set is the maximal ideal mM of OM and the group operation is defined by the formula
  x+F
  y = F(x, y). The group F(mM) can be regarded as an EndO
  K(F)[G]-module with the
  natural action of G. The case of the multiplicative formal group law F = Fm is considered
  in detail in the paper of Borevich (1965), where the author describes the above-mentioned
  module structure by generators and defining relations when K = Qp and M/L is a cyclic
  p-extension. It is well known that if F is a Lubin—Tate formal group law, then there is
  an embedding of rings OK  → EndO
  K(F), which makes it possible to consider F(mM)
  as an OK[G]-module. One natural generalization to the case of Lubin—Tate formal group
  laws is the paper of Vostokov (2014), where the structure of the OK[G]-module F(mM)
  is described in the case of an unramified cyclic p-extension of irregular fields M and L
  with equal indices of irregularity. Let K0/Qp be a finite extension, K/K0 be an unramified
  extension, π ∈ K0 be a uniformizing element in K0, F be a Honda formal group of finite
  height over the ring OK for the extension K/K0 and the prime π. Let Kalg be a fixed
  algebraic closure of K, mKalg be the valuation ideal, Wn
  F = ker[πn]F ⊂ F(mKalg ) be the
  πn-torsion submodule, and WF =
   ∞
  n=1Wn
  F . In the present paper, we generalize the results
  of Vostokov to the case of a Honda formal group F. In particular, we describe the structure
  of the OK0 [G]-module F(mM) in the case of an unramified p-extension M/L for which the
  condition WF ∩ F(mL) = WF ∩ F(mM) = Ws
  F is valid for some s ≥ 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РНФ (грант 16-11-10200).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: local field
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: unramified extension
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: formal group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Galois module
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Honda formal group in unramified p-extension of local field as Galois module
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Akopyan.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15123/1/01-Akopyan.pdf
resources.format: Adobe PDF
resources.size: 317,76 kB