On the Euler-Poincaré characteristics of finite dimensional $p$-adic Galois representations

John Coates; Ramdorai Sujatha; Jean-Pierre Wintenberger

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Lifting Galois representations and a conjecture of Fontaine and Mazur.

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The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead...