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In this paper we introduce the word "fresco" to denote a$[\lambda]-$primitive monogenic geometric (a,b)-module. The study of this"basic object" (generalized Brieskorn module with one generator) whichcorresponds to the minimal filtered (regular) differential equation satisfiedby a relative de Rham cohomology class, began in [B.09] where the firststructure theorems are proved. Then in [B.10] we introduced the notion of themewhich corresponds in the $[\lambda]-$primitive case to frescos having a uniqueJordan-H{\"o}lder sequence. Themes correspond to asymptotic expansion of agiven vanishing period, so to the image of a fresco in the module of asymptoticexpansions. For a fixed relative de Rham cohomology class (for instance givenby a smooth differential form $d-$closed and $df-$closed) each choice of avanishing cycle in the spectral eigenspace of the monodromy for the eigenvalue$exp(-2i\pi.\lambda)$ produces a $[\lambda]-$primitive theme, which is aquotient of the fresco associated to the given relative de Rham class itself.So the problem to determine which theme is a quotient of a given fresco isimportant to deduce possible asymptotic expansions of the various vanishingperiod integrals associated to a given relative de Rham class when we changethe choice of the vanishing cycle. In the appendix we prove a general existenceresult which naturally associate a fresco to any relative de Rham cohomologyclass of a proper holomorphic function of a complex manifold onto a disc.

Asymptotics of a vanishing period : the quotient themes of a given fresco