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Note on the Stokes structure of Fourier transform. (English) Zbl 1201.32016
The author considers a meromorphic flat bundle on $$\mathbb{P}^1$$ $$(V,\nabla)$$ and the $$D$$-module Four$$(V)$$ on $$\mathbb{P}^1$$ obtained as the Fourier transform of $$(V,\nabla)$$. He studies the structure of Four$$(V)$$, following the homology theory introduced by Bloch and Esnault, his main purpose being to understand the part of an unpublished paper by Beilinson, Bloch, Deligne and Esnault “Periods for irregular connections on curves” related with the Stokes structure. This is an apparently different description of that given by Malgrange. Among other things, the paper shows that the space $$\psi$$ (Gr Four($$V$$)) of the multi-valued flat sections of the graded meromorphic flat bundle Gr Four($$V$$) is equipped with a $$(K,k)$$ structure ($$K$$ and $$k$$ being certain fields) which is described in terms of the data around the poles of $$(V,\nabla)$$.

##### MSC:
 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 14F40 de Rham cohomology and algebraic geometry
##### Keywords:
Fourier transform; Stokes structure
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