TY - JOUR

T1 - Explicit form of the Hilbert symbol for polynomial formal groups

AU - Vostokov, S.

AU - Volkov, V.

PY - 2015

Y1 - 2015

N2 - © 2015 American Mathematical Society. Let K be a local field, c a unit in K, and Fc(X, Y) = X + Y + cXY a polynomial formal group that gives rise to a formal module Fc(M) on the maximal ideal in the ring of integers of K. Assume that K contains the group μFc,n of the roots of isogeny [pn]c(X). The natural Hilbert symbol ( · , · )c : K*×Fc(M) → μFc,n is defined over the module F(M). An explicit formula for ( · , · )c is constructed.

AB - © 2015 American Mathematical Society. Let K be a local field, c a unit in K, and Fc(X, Y) = X + Y + cXY a polynomial formal group that gives rise to a formal module Fc(M) on the maximal ideal in the ring of integers of K. Assume that K contains the group μFc,n of the roots of isogeny [pn]c(X). The natural Hilbert symbol ( · , · )c : K*×Fc(M) → μFc,n is defined over the module F(M). An explicit formula for ( · , · )c is constructed.

U2 - 10.1090/spmj/1358

DO - 10.1090/spmj/1358

M3 - Article

VL - 26

SP - 785

EP - 796

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -