Périodes évanescentes et $a,b$-modules monogènesReport as inadecuate



 Périodes évanescentes et $a,b$-modules monogènes


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In order to describe the asymptotic behaviour of a vanishing period in a one parameter family we introduce and use a very simple algebraic structure : regular geometric a,b-modules generated as left $\A-$modules by one element. The idea is to use not the full Brieskorn module associated to the Gauss-Manin connection but a minimal regular differential equation satisfied by the period integral we are interested in. We show that the Bernstein polynomial associated is quite simple to compute for such a,b-modules and give a precise description of the exponents which appears in the asymptotic expansion which avoids integral shifts. We show a couple of explicit computations in some classical but not so easy examples.



Author: Daniel Barlet

Source: https://archive.org/







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