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de Rham representations and universal norms. (Représentations de de Rham et normes universelles.) (French) Zbl 1122.11036
The author computes the module of universal norms for a de Rham \(p\)-adic representation (Théorème A). His method uses ideas from [B. Perrin-Riou, J. Am. Math. Soc. 13, No. 3, 533–551 (2000; Zbl 1024.11069); Mém. Soc. Math. Fr., Nouv. Sér. 84 (2001; Zbl 1031.11064)] (cases of cristalline and semistable representations) and from [L. Berger, [Invent. Math. 148, No. 2, 219–284 (2002; Zbl 1113.14016); Doc. Math., J. DMV Extra Vol., 99–129 (2003; Zbl 1064.11077)]. The theory of \((\varphi,\Gamma)\)-modules (Cherbonnier-Colmez’s reciprocity formula) allows to extend these ideas to a general case of a de Rham representation.

MSC:
11F80 Galois representations
11R23 Iwasawa theory
11S25 Galois cohomology
12H25 \(p\)-adic differential equations
14F30 \(p\)-adic cohomology, crystalline cohomology
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