Generators for the tautological algebra of the moduli space of curves

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Cohomological structure of the mapping class group and beyond (2005, background): “that the images of the above homomorphisms ρ∗ 2 are precisely the tautological algebras. Here the conceptofthegeneralizedMorita-Mumfordclasses deﬁned byKawazumi [48] played an important role. Then in [82], the eﬀect ofunstable degenerations of Sp-modules appearing in (7) was analized and in particul”
Resolutions of moduli spaces and homological stability (2009, background): “Morita [19] has shown the classes κ1, .”
Tautological and non-tautological cohomology of the moduli space of curves (2011, background): “A complete (conjectural) structure of R(Mg) is proposed in [18] with important advances made in [41, 47, 49].”
Normal Functions and the Geometry of Moduli Spaces of Curves (2011, methodology): “This formula, modulo boundary terms, was proved by Morita [30, (1.7)].”