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There have been many works to generalize the Nevanlinna theory (especially, his second main theorem) to higher dimensional case (cf., e.g., [5], [17], [21]). While the so called equidimensional holomorphic or meromorphic mappings / : W—>V between algebraic varieties have been well studied, we do not know very much about f:W-+V with άimW<άimV (cf. Noguchi [13], [14] and Siu [20]). So far, we have to put some special restriction on target spaces or on the divisors of the target spaces. In this paper, we will establish an inequality of the second main theorem type for meromorphic mappings into a compactification of a locally symmetric space. Let 3) be a bounded symmetric domain in C m and Γ a neat arithmetic discrete subgroup of the holomorphic transformation group Aut (3)) of 3). Let / : C->Γ\β)

Value distribution of meromorphic mappings into compactified locally symmetric spaces