The Rational Cohomology Ring of the Moduli Space of Abelian 3-folds
نویسنده
چکیده
In this note we compute the rational cohomology ring of Sp3(Z), or equivalently, of A3, the moduli space of principally polarized abelian 3-folds. Denote the Q-Hodge structure of dimension 1 and weight −2n by Q(n). (For those not interested in Hodge theory, just interpret this as one copy of Q.) Denote by λ the first Chern class in H(A3;Q) of the Hodge bundle detπ∗Ω 1 associated to the projection π of the universal abelian 3-fold to A3. Theorem 1. The cohomology groups of A3 are given by
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