Cohomology of arithmetic families of (𝜑,Γ)-modules

Kedlaya, Kiran¹ ; Pottharst, Jonathan² ; Xiao, Liang³

¹ Department of Mathematics, University of California, San Diego, La Jolla, California 92093
² 5 Redwood Street, Boston, Massachusetts 02122
³ Department of Mathematics, University of California, Irvine, Rowland Hall 340, Irvine, California 92697

Journal of the American Mathematical Society, Tome 27 (2014) no. 4, pp. 1043-1115

Résumé

We prove the finiteness and compatibility with base change of the $(\varphi , \Gamma )$-cohomology and the Iwasawa cohomology of arithmetic families of $(\varphi , \Gamma )$-modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually trianguline as a family over a large subspace. In the case of the Coleman-Mazur eigencurve, we determine the behavior at all points.

Détail

DOI : 10.1090/S0894-0347-2014-00794-3

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