Pixton's relations and the tautological ring
-- Dmitry Zakharov, September 30, 2016
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The tautological ring of the moduli space of curves M<sub>g</sub> is a natural
subring of either the cohomology or the Chow ring that is generated by
a collection of natural classes. A number of vanishing results have
been established about the tautological ring of M<sub>g</sub> and its various
compactifications. I will show that these results can be derived in a
uniform and constructive way from Pixton's double ramification cycle
relations, which were recently established by Clader and Janda, and I
will discuss what further consequences Pixton's relations may have.