TY - JOUR

T1 - THE HILBERT PAIRING FOR FORMAL GROUPS OVER Σ-RINGS

AU - Bondarko, M.V.

AU - Vostokov, S.V.

AU - Lorenz, F.

PY - 2006

Y1 - 2006

N2 - In the paper, formal groups over the rings of integers of σ-fields are studied. These fields were constructed by the first author in a previous paper. They are a generalization of the inertia field of a classical local field to an arbitrary complete discrete valuation field of characteristic zero. An analog of Honda’s theory for such formal groups is constructed. The arithmetic of the group of points in an extension of a σ-field that contains sufficiently many torsion points is studied. Using the classification of formal groups and the arithmetic results obtained, an explicit formula for the Hilbert pairing for formal groups over σ-fields is proved. Bibliography: 16 titles. © 2006 Springer Science+Business Media, Inc.

AB - In the paper, formal groups over the rings of integers of σ-fields are studied. These fields were constructed by the first author in a previous paper. They are a generalization of the inertia field of a classical local field to an arbitrary complete discrete valuation field of characteristic zero. An analog of Honda’s theory for such formal groups is constructed. The arithmetic of the group of points in an extension of a σ-field that contains sufficiently many torsion points is studied. Using the classification of formal groups and the arithmetic results obtained, an explicit formula for the Hilbert pairing for formal groups over σ-fields is proved. Bibliography: 16 titles. © 2006 Springer Science+Business Media, Inc.

M3 - Article

SP - 2445

EP - 2476

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -