Generators for the tautological algebra of the moduli space of curves. (Q1868039)

The author proves that the tautological algebra in cohomology of the moduli space \(M_g\) of smooth projective curves of genus \(g\) is generated by the first \([g/3]\) Mumford-Morita-Miller classes. This solves a part of \textit{C. Faber}'s conjecture [Moduli of curves and Abelian varieties. Aspects Math. E 33, 109--129 (1999; Zbl 0978.14029)] concerning the structure of the tautological algebra affirmatively. More precisely, for any \(k\) he writes the kth Mumford-Morita-Miller class \(e_k\) as an explicit polynomial in the lower classes for all genera \(g=3k-1,3k-2,\dots,2\).