Study of the analytic fundamental group via differential methods

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Project objective

Research objectives and content The aim of the research is to study the analytic fun- damental group of punctured disc imbedded in the rigid analytic variety associated to the affine line over a p-adic field. A better understanding of this group is required, if we want to find a good category of etale analytic coefficient sheaves, which would be stable under the usual six coho- mological operations. and moreover would be preserved by the itale Fourier transform (which I defined first in my PhD thesis and studied subsequently in the paper cited in the detailed research proposal). The method proposed is to associate to any padic lisse itale sheaf, a certain p-adic differential equation, in a func- torial way. This idea is due originally to J.M. Fontaine, who implemented it in the case of padic representations of local fields, and asked for a global analogue of his construction. Training conlent (obyive, benefit and expecteJ impact) For the completion of the project, I will need to get acquainted with a variety of techniques, such as Faltings's work on the mysterious functor, Fontaine-Laffaille's theory and with the work of Christol-Mehbkout on the index of padic differential equations, to name a few.

Original text from CORDIS.

Participants

• UNIVERSITE PIERRE ET MARIE CURIE - PARIS VI · PARISCoordinatorFrance
• Not availableCity levelItaly

Links

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