What are Robba rings and why are they important?

by Sameer Kulkarni   Last Updated October 17, 2018 06:20 AM - source

If we study $p$-adic Galois representations we come across the so called ``Robba rings'', defined as the ring of Laurent series which converge in some annulus $\{z| \,\,R<|z|<1\}$ for some positive number $R<1$. I looked at the literature a bit to see why such rings are important. But I could not find any that explains the genesis of the concept itself. Apparently these rings are intimately associated to phi-gamma modules. Any reference or any hint why Robba rings are studied? Perhaps the motivation is from the usual comples analysis?

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Updated June 15, 2018 21:20 PM