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An introduction to the theory of \(p\)-adic representations. (English) Zbl 1118.11028

Adolphson, Alan (ed.) et al., Geometric aspects of Dwork theory. Vol. I, II. Berlin: Walter de Gruyter (ISBN 3-11-017478-2/hbk). 255-292 (2004).
This is a succinct guide to some recent developments in the theory of \(p\)-adic representations of \(p\)-adic fields (\(p\) prime). It goes into the construction of Fontaine’s rings of periods, his theory of \((\varphi,\Gamma)\)-modules, and culminates with a discussion of the \(p\)-adic local monodromy theorem, the analogue of Grothendieck’s \(l\)-adic (\(l\) prime \(\neq p\)) local “potential semistability” theorem. Each section ends with judicious references to the literature.
For the entire collection see [Zbl 1047.14001].

MSC:

11F80 Galois representations
11S25 Galois cohomology
14F30 \(p\)-adic cohomology, crystalline cohomology
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