Geodesic
An equivariant main conjecture in Iwasawa theory and the Coates-Sinnott conjecture
Documenta mathematica, Tome 18 (2013), pp. 749-783
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We formulate and prove an Equivariant Main Conjecture (EMC) for all prime numbers p under the assumptions μ=0 and the validity of the 2-adic Main Conjecture in Iwasawa theory citeWi. This equivariant version coincides with the version, which Ritter and Weiss formulated and proved for odd p under the assumption μ=0 in citeRW2. Our proof combines the approach of Ritter and Weiss with ideas and techniques used by Greither and Popescu in citeGP2 in a recent proof of an equivalent formulation of the above EMC under the same assumptions (p odd and μ=0) as in citeRW2. As an application of the EMC we prove the Coates-Sinnott Conjecture, again assuming μ=0 and the 2-adic Main Conjecture.
DOI : 10.4171/dm/413
Classification : 11R23, 11R33, 11R34, 11R42, 11R70, 14F42
Mots-clés : Iwasawa theory, motivic cohomology, algebraic K-theory, global and p-adic L-functions, Fitting ideals 
@article{10_4171_dm_413,
     author = {Reza Taleb},
     title = {An equivariant main conjecture in {Iwasawa} theory and the {Coates-Sinnott} conjecture},
     journal = {Documenta mathematica},
     pages = {749--783},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/413},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/413/}
}
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Reza Taleb. An equivariant main conjecture in Iwasawa theory and the Coates-Sinnott conjecture. Documenta mathematica, Tome 18 (2013), pp. 749-783. doi: 10.4171/dm/413

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