The Lubin–Tate Formal Module in a Cyclic Unramified P-Extension as a Galois Module

Vostokov, S. V.; Nekrasov, Ilia

doi:10.1007/s10958-016-3113-6

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…Consider it modulo Π 2 , then we get Tr M/L ξ = Π mod Π 2 . Therefore we get (for more details [9] Lemma 6) ξ = Πχ mod Π 2…”

Section: Calculating λωmentioning

confidence: 96%

“…We will not initially assume that the formula is known, but by successive transformations we will derive it from scratch, so that it will be clear where it comes from. To do this, we turn to a non-standard system of generators and relations for these purposes, which was constructed by Borevich [8] and Iwasawa [7] for the classical case of an unramified p−extension of a local field and further generalized to the case of formal modules over unramified extensions [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

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Artin-Hasse formula for $p^m-$primary elements

Polyakov¹

2022

Preprint

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Using Borevich's system of generators and relations, the classical Artin-Hasse formula is obtained from scratch in the case when taking p-th root of the second argument of the Hilbert symbol gives an unramified p-extension of the same degree of irregularity. Under the same assumptions, in the case of Lubin-Tate formal groups, an expression for the Hilbert symbol is obtained in terms of the expansion of elements by the same system of generators.

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“…Consider it modulo Π 2 , then we get Tr M/L ξ = Π mod Π 2 . Therefore we get (for more details [9] Lemma 6) ξ = Πχ mod Π 2…”

Section: Calculating λωmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Artin-Hasse formula for $p^m-$primary elements

Polyakov¹

2022

Preprint

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“…The next stop in the course of investigations was the joint work of S.V.Vostokov and I.I.Nekrasov [8], where they generalized the aforementioned theorem to the case of Lubin-Tate formal groups. More precisely, they managed to prove the following Theorem (Vostokov-Nekrasov, 2014).…”

Section: Introductionmentioning

confidence: 99%

Honda formal group as Galois module in unramified extensions of local fields

Hakobyan¹,

Востоков²

2018

Preprint

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For given rational prime number p consider the tower of finite extensions of fields K 0 /Q p , K/K 0 , L/K, M/L, where K/K 0 is unramified and M/L is a Galois extension with Galois group G. Suppose one dimensional Honda formal group over the ring O K , relative to the extension K/K 0 and uniformizer π ∈ K 0 is given. The operation x + F y = F (x, y) sets a new structure of abelian group on the maximal ideal p M of the ring O M which we will denote by F (p M ). In this paper the structure of F (p M ) as O K 0 [G]-module is studied for specific unramified p-extensions M/L.

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