AN EQUIVARIANT MAIN CONJECTURE IN IWASAWA THEORY AND THE COATES-SINNOTT CONJECTURE

作者：Taleb Reza^*

来源：Documenta Mathematica, 2013, 18: 749-783.

DOI：10.4171/dm/413

• Iwasawa theory
• global and p-adic L-functions
• motivic cohomology
• algebraic K-theory
• Fitting ideals

We formulate and prove an Equivariant Main Conjecture (EMC) for all prime numbers p under the assumptions mu = 0 and the validity of the 2-adic Main Conjecture in Iwasawa theory [47]. This equivariant version coincides with the version, which Ritter and Weiss formulated and proved for odd p under the assumption mu = 0 in [35]. Our proof combines the approach of Ritter and Weiss with ideas and techniques used by Greither and Popescu in [15] in a recent proof of an equivalent formulation of the above EMC under the same assumptions (p odd and mu = 0) as in [35]. As an application of the EMC we prove the Coates-Sinnott Conjecture, again assuming mu = 0 and the 2-adic Main Conjecture.

• 出版日期2013