title: Formal groups over sub-rings of the ring of integers of a multidimensional local field
metadata.name: dc.contributor.author
metadata.value: Madunts, Aleksandra I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vostokov, Sergey V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vostokova, Regina P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T08:31:07Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T08:31:07Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Madunts A. I., Vostokov S.V., Vostokova R.P. Formal groups over sub-rings of the ring of integers of a multidimensional local field. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 1, pp. 88–97.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org /10.21638/11701/spbu01.2019.106
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15539
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the work we construct so-called convergence rings for the ring of integers of a multidi-mensional local ﬁeld. The convergence ring is a sub-ring of the ring of integers having the property that any power series with coeﬃcients from the sub-ring converges when replacing a variable on an arbitrary element of the maximum ideal. The properties of convergence rings and an explicit formula for their construction are derived. Note that the multidi-mensional case is fundamentally diﬀerent from the case of the classical (one-dimensional) local ﬁeld, where the convergence ring is the whole ring of integers. Next, we consider a multidimensional local ﬁeld with zero characteristic of the penultimate residue ﬁeld. For each convergence ring of such a ﬁeld, we introduce a homomorphism that allows for a power series with coeﬃcients from the ring to construct a formal group over the same ring with a logarithm having coeﬃcients from the ﬁeld, and we give an explicit formula for the coeﬃcients. In addition, we constructe a generalization of the formal Lubin-Tate group over this ring, study the endomorphisms of these formal groups and derive a criterion for their isomorphism. We prove a one-to-one correspondence between formal groups created by ring homomorphism and by isogeny. Also for any ﬁnite extension of a multidimensional local ﬁeld with zero characteristic of the penultimate residue ﬁeld, we considere the point group generated by the corresponding Lubin-Tate formal group.
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 6 (64); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: multidimensional local field
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lubin—Tate formal group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convergence of power series
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Formal groups over sub-rings of the ring of integers of a multidimensional local field
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 88-97.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15539/1/88-97.pdf
resources.format: Adobe PDF
resources.size: 295,5 kB