Introduction.-Let R be a complete discrete valuation ring of characteristic zero, m the valuation ideal of R, k = R/m the residue field, and QR the fraction field of R. The principal case of interest arises if R is the completion of a ring of algebraic integers with respect to one of its prime ideals; but the equal characteristic case or even the particular case where R is a field and m is the zero ideal is not entirely without interest.Let V be a nonsingular variety defined over k. We shall attach to V certain
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