Frobenius manifolds near the discriminant and relations in the tautological ring

Abstract

We give a criterion for extending a generically semisimple (not necessarily conformal) Frobenius manifold locally near a smooth point of the discriminant to a cohomological field theory. As an application, we show that a large set of tautological relations related to the Givental--Teleman classification for any generically semisimple cohomological field theories follow from Pixton's generalized Faber--Zagier relations.