Mathematics – Number Theory
Scientific paper
2010-09-20
Mathematics
Number Theory
Scientific paper
In Part I we review some specific properties of the $\Lambda$-modules in Iwasawa theory, which add structure to the general properties of Noetherian $\Lambda$-torsion modules. Part II deals with Kummer theory and gives a detailed construction of the Iwasawa linear space. This provides a new, simpler proof of the conjectures of Leopoldt and Gross for CM extensions. Using a construction of Thaine, we then prove that $\lambda^+ = 0$ in these fields, thus proving a part of Greenberg's conjecture - the fact $\mu^+ = 0$ still has to be shown. In the Appendices we give some elementary partial proofs of the main facts proved using Iwasawa's linear space. These two papers do not give proofs for non CM fields, and the reader interested in methods for dealing with this case is referred to the "$T and T^*$" paper on this arxive. This methods will be integrated in the Snoqit series.
No associations
LandOfFree
Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $Λ[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $Λ[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $Λ[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-263940