280 research outputs found
Comparison Isomorphisms for Smooth Formal Schemes
For a smooth proper scheme or formal scheme over an unramified, complete DVR
of mixed characteristics we prove a comparison isomorphism relating etale
cohomology of the generic fiber with values in a crystalline etale sheaf to the
crystalline cohomology of its special fiber with values in the associated
F-isocrystal
Big image of Galois representations associated with finite slope -adic families of modular forms
We consider the Galois representation associated with a finite slope -adic
family of modular forms. We prove that the Lie algebra of its image contains a
congruence Lie subalgebra of a non-trivial level. We describe the largest such
level in terms of the congruences of the family with -adic CM forms.Comment: 23 pages; revision of Section 2 (see Remark 2.4) and improvement of
Proposition 4.14, plus minor changes. Published in "Elliptic Curves, Modular
Forms and Iwasawa Theory. In Honour of John H. Coates' 70th Birthday,
Cambridge, UK, March 2015", Springer Proceedings in Mathematics & Statistics,
Vol. 188, 201
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