Wach modules, regulator maps, and epsilon-isomorphisms in families
Rebecca Bellovin, Otmar Venjakob

TL;DR
This paper proves the local epsilon-isomorphism conjecture for certain crystalline G_Qp-representations, extending previous work and showing independence of triangulation choices in families, using Wach modules and regulator maps.
Contribution
It establishes the epsilon-isomorphism conjecture for crystalline families, generalizing prior results and constructing Wach modules in a new family context.
Findings
Proved the epsilon-isomorphism conjecture for specific crystalline families.
Constructed families of Wach modules generalizing previous work.
Showed independence of epsilon-isomorphism from triangulation choices.
Abstract
We prove the local epsilon-isomorphism conjecture of Fukaya and Kato [FK06] for certain crystalline families of G_Qp-representations. This conjecture can be regarded as a local analogue of the Iwasawa main conjecture for families. Our work extends earlier work of Kato for rank-1 modules (cf. [Ven13]), of Benois and Berger for crystalline G_Qp-representations with respect to the cyclotomic extension (cf. [BB08]), as well as of Loeffler, Venjakob, and Zerbes (cf. [LVZ13]) for crystalline G_Qp- representations with respect to abelian p-adic Lie extensions of Qp. Nakamura [Nak13, Nak14] has also formulated a version of the epsilon-conjecture for affinoid families of (phi,Gamma)-modules over the Robba ring, and proved his conjecture in the rank-1 case. He used this case to construct an epsilon-isomorphism for families of trianguline (phi,Gamma)-modules, depending on a fixed triangulation.…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
