Holmstrom Euler system

See the book of Coates and Sujatha.

MR1749177 (2001g:11170) Rubin, Karl Euler systems.

Scholl: Article in the LMS volume on Galois reps, I think

Arizona Winter School

http://mathoverflow.net/questions/11421/is-higher-k-functor-the-derived-functor-of-k0

[arXiv:0706.0377] Λ\Lambda-adic Kolyvagin systems from arXiv Front: math.NT by Kazim Buyukboduk In this paper, we study the deformations of Kolyvagin systems that are known to exist in a wide variety of cases, by the work of B. Howard, B. Mazur, and K. Rubin for the residual Galois representations, along the cyclotomic Iwasawa algebra. We prove, under certain technical hypotheses, that a cyclotomic deformation of a Kolyvagin system exists. We also briefly discuss how our techniques could be extended to prove that one could deform Kolyvagin systems for other deformations as well

We discuss several applications of this result, particularly relation of these Λ\Lambda-adic Kolyvagin systems to p-adic L-functions (in view of the conjectures of Perrin-Riou on p-adic L-functions) and applications to main conjectures; also applications to the study of Iwasawa theory of Rubin-Stark units.

arXiv:1103.5982 On Euler systems of rank rr and their Kolyvagin systems from arXiv Front: math.NT by Kazim Buyukboduk In this paper we set up a general Kolyvagin system machinery for Euler systems of rank r (in the sense of Perrin-Riou) associated to a large class of Galois representations, building on our previous work on Kolyvagin systems of Rubin-Stark units and generalizing the results of Kato, Rubin and Perrin-Riou. Our machinery produces a bound on the size of the classical Selmer group attached to a Galoys representation T (that satisfies certain technical hypotheses) in terms of a certain r \times r determinant; a bound which remarkably goes hand in hand with Bloch-Kato conjectures. At the end, we present an application based on a conjecture of Perrin-Riou on p-adic L-functions, which lends further evidence to Bloch-Kato conjectures.

nLab page on Euler system

Created on June 9, 2014 at 21:16:13 by Andreas Holmström