TY - JOUR

T1 - DEGENERATION OF THE HILBERT PAIRING IN FORMAL GROUPS OVER LOCAL FIELDS

AU - Vostokov, S. V.

AU - Vostokova, R. P.

AU - Podkopaeva, O. Yu.

PY - 2016

Y1 - 2016

N2 - For an arbitrary local field K (a finite extension of the field Qp) and an arbitrary formal group law F over K, we consider an analog cF of the classical Hilbert pairing. A theorem by S. V. Vostokov and I. B. Fesenko says that if the pairing cF has a certain fundamental symbol property for all Lubin—Tate formal groups, then cF = 0. We generalize the theorem of Vostokov—Fesenko to a wider class of formal groups. Our first result concerns formal groups that are defined over the ring OK of integers of K and have a fixed ring O0 of endomorphisms, where O0 is a subring of OK. We prove that if the symbol cF has the above-mentioned symbol property, then cF = 0. Our second result strengthens the first one in the case of Honda formal groups. The paper consists of three sections. After a short introduction in Sec. 1, we recall basic definitions and facts concerning formal group laws in Sec. 2. In Sec. 3, we state and prove two main results of the paper (Theorems 1 and 2). Refs 8

AB - For an arbitrary local field K (a finite extension of the field Qp) and an arbitrary formal group law F over K, we consider an analog cF of the classical Hilbert pairing. A theorem by S. V. Vostokov and I. B. Fesenko says that if the pairing cF has a certain fundamental symbol property for all Lubin—Tate formal groups, then cF = 0. We generalize the theorem of Vostokov—Fesenko to a wider class of formal groups. Our first result concerns formal groups that are defined over the ring OK of integers of K and have a fixed ring O0 of endomorphisms, where O0 is a subring of OK. We prove that if the symbol cF has the above-mentioned symbol property, then cF = 0. Our second result strengthens the first one in the case of Honda formal groups. The paper consists of three sections. After a short introduction in Sec. 1, we recall basic definitions and facts concerning formal group laws in Sec. 2. In Sec. 3, we state and prove two main results of the paper (Theorems 1 and 2). Refs 8

KW - Hilbert pairing

KW - formal groups

KW - local fields

KW - Steinberg relation

KW - формальная группа

KW - формальный модуль

KW - изогения

KW - спаривание гильберта

UR - http://vestnik.spbu.ru/html16/s01/s01v1/07.pdf

M3 - Article

VL - 3(61)

SP - 59

EP - 66

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ

SN - 1025-3106

IS - 1

ER -