title: Iwasawa Theory for One-Parameter Families of Motives
creator: Barth, Peter
subject: 510
subject: 510 Mathematics
description: In this thesis we build on the work of Fukaya and Kato in which they presented equivariant Tamagawa Number conjectures that implied a very general (noncommutative) Iwasawa main conjecture for rather general motives. We apply their methods to the case of one-parameter families of motives to derive a main conjecture for such families (theorem 4.31). On our way there we get some unconditional results on the variation of the (algebraic) $lambda$- and the $mu$-invariant in many cases (theorem 3.33 and corollary 3.34). We focus on the results dealing with Selmer complexes instead of the more classical notion of Selmer groups. However, where possible we give the connection to the classical notions. The final chapter deals with the deformation theory of the representations occurring in our theory and the existence of one-parameter families. In particular we recover and generalize some results on the variation of Iwasawa invariants in Hida families.
date: 2011
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/12647/1/OneParamterFam.pdf
identifier: DOI:10.11588/heidok.00012647
identifier: urn:nbn:de:bsz:16-opus-126472
identifier:   Barth, Peter  (2011) Iwasawa Theory for One-Parameter Families of Motives.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/12647/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng