TL;DR
This survey explains the theory of trianguline p-adic Galois representations, their properties, and examples in arithmetic geometry, highlighting their role within the framework of (phi,Gamma)-modules.
Contribution
It provides a comprehensive overview of trianguline representations and their connection to (phi,Gamma)-modules, including new examples in arithmetic geometry.
Findings
Trianguline representations are a significant class of p-adic Galois representations.
They are characterized via (phi,Gamma)-modules.
Examples demonstrate their relevance in arithmetic geometry.
Abstract
Trianguline representations are a certain class of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (phi,Gamma)-modules. In this survey, we explain the theory of (phi,Gamma)-modules and the definition and properties of trianguline representations. After that, we give some examples of their occurrence in arithmetic geometry.
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