On the norm property of the Hilbert symbol for polynomial formal modules in a multidimensional local field


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In a two-dimensional local field K containing the pth root of unity, a polynomial formal group Fc(X, Y) = X + Y + cXY acting on the maximal ideal M of the ring of integers бK and a constructive Hilbert pairing {·, ·}c: K2(K) × Fc(M) → <ξ>c, where <ξ>c is the module of roots of [p]c (pth degree isogeny of Fc) with respect to formal summation are considered. For the extension of two-dimensional local fields L/K, a norm map of Milnor groups Norm: K2(L) → K2(K) is considered. Its images are called norms in K2(L). The main finding of this study is that the norm property of pairing {·, ·}c: {x,β}c: = 0 ⇔ x is a norm in K2(K([p]c-1(β))), where [p]c-1(β) are the roots of the equation [p]c = β, is checked constructively.

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V. Volkov

St. Petersburg State University

编辑信件的主要联系方式.
Email: vladvolkov239@gmail.com
俄罗斯联邦, Universitetskaya nab. 7/9, St. Petersburg, 199034

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