Titlebook: Introduction to Stokes Structures; Claude Sabbah Book 2013 Springer-Verlag Berlin Heidelberg 2013 34M40, 32C38, 35A27.Meromorphic connecti

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Apoptosis

Stokes-Perverse Sheaves on Riemann Surfacesr will be an equivalence between holonomic .-modules on the Riemann surface and Stokes-perverse sheaves on it. If . is a subfield of ., this allows one to speak of a .-structure on a holonomic .-module when the corresponding Stokes-perverse is defined over ..

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Applications of the Riemann–Hilbert Correspondence to Holonomic Distributionsis also holonomic. As an application, we make explicit the local expression of a holonomic distribution, that is, a distribution on . (in Schwartz’ sense) which is solution to a nonzero holomorphic differential equation on .. The conclusion is that working with . objects hides the Stokes phenomenon.

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Irregular Nearby Cyclesbraic case. We give a new proof of this theorem when the support of the holonomic .-module has dimension two, which holds in the complex analytic setting and which makes more precise the non-vanishing nearby cycles.

Largess

Nearby Cycles of Stokes-Filtered Local Systems is contained in the normal crossing divisor .. We then show that the Riemann–Hilbert correspondence of Chap. 12 is compatible with taking nearby cycles, either in the sense of irregular nearby cycles for meromorphic flat bundles as defined in Chap. 14, or as defined for Stokes-filtered local systems in this chapter.

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音乐等

Introduction to Stokes Structures978-3-642-31695-1Series ISSN 0075-8434 Series E-ISSN 1617-9692

官僚统治

Stokes-Filtered Local Systems in Dimension OneWe consider Stokes filtrations on local systems on ... We review some of the definitions of the previous chapter in this case and make explicit the supplementary properties coming from this particular case. This chapter can be read independently of Chap. 1.

Gullible

Abelianity and StrictnessWe prove that the category of .-Stokes-filtered local systems on .. is abelian. The main ingredient, together with vanishing properties of the cohomology, is the introduction of the level structure. Abelianity is also a consequence of the Riemann–Hilbert correspondence considered in Chap. 5, but it is instructive to prove it over the base field ..