Local epsilon isomorphisms

Abstract

In this paper, we prove the "local epsilon-isomorphism conjecture" of Fukaya and Kato for a particular class of Galois modules obtained by tensoring a Zp-lattice in a crystalline representation of the Galois group of Qp with a representation of an abelian quotient of the Galois group with values in a suitable p-adic local ring. This can be regarded as a local analogue of the Iwasawa main conjecture for abelian p-adic Lie extensions of Qp, extending earlier work of Benois and Berger for the cyclotomic extension. We show that such an epsilon-isomorphism can be constructed using the Perrin-Riou regulator map, or its extension to the 2-variable case due to the first and third authors.

References in corpus (3)

• Iwasawa theory and p-adic L-functions over ${\mathbf{Z}}_p^2$-extensions
• On Kato's local epsilon-isomorphism Conjecture for rank one Iwasawa modules
• A generalization of Kato's local epsilon-conjecture for (phi,Gamma)-modules over the Robba ring

Cited by in corpus (9)

• Rankin--Eisenstein classes for modular forms
• Rankin-Selberg Euler systems and p-adic interpolation
• Euler systems with local conditions
• A generalization of Kato's local epsilon-conjecture for (phi,Gamma)-modules over the Robba ring
• An equivariant Iwasawa main conjecture for local fields
• Eisenstein degeneration of Euler systems
• $\epsilon$-isomorphisms for rank one $(\phi ,\Gamma )$-modules over Lubin-Tate Robba rings
• Local epsilon-isomorphisms for rank two p-adic representations of Gal(overline{Q}_p/Q_p) and a functional equation of Kato's Euler system
• Exceptional zero formulae and a conjecture of Perrin-Riou