Abstract
The main goal of this article is to discuss the relevant background needed to state the noncommutative main conjecture for certain totally real p-adic Lie extensions, and to make the important reduction to the case when the Galois group of the p-adic Lie extension is of dimension one and pro-p.
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H. Bass, Algebraic K-Theory (W. A. Benjamin, Inc., New York/Amsterdam, 1968)
J.-E. Björk, Filtered Noetherian rings, in Noetherian Rings and Their Applications (Oberwolfach, 1983), 5997. Mathematical Surveys and Monographs, vol. 24 (American Mathematical Society, Providence, 1987)
D. Burns, On main conjectures in noncommutative Iwasawa theory and related conjectures, preprint (2010) http://www.mth.kcl.ac.uk/staff/dj_burns/newdbpublist.html
J. Coates, D. Kim, Introduction to the work of M. Kakde on the non-commutative main conjectures for totally real fields, This volume
J. Coates, T. Fukaya, K. Kato, R. Sujatha, O. Venjakob, The GL 2 main conjecture for elliptic curves without complex multiplication. Publ. Math. IHES 101, 163–208 (2005)
C. Curtis, I. Reiner, Methods of Representation Theory with applications to Finite Groups and Orders (Wiley, New York, 1981)
T. Fukaya, K. Kato, A formulation of conjectures on p-adic zeta functions in noncommutative Iwasawa theory, in Proceedings of the St. Petersburg Mathematical Society, vol. 12, ed. by N.N. Uraltseva (American Mathematical Society, Providence, 2006), pp. 1–85
M. Kakde, The Main Conjecture of Iwasawa theory for totally real fields, preprint (2011)
J. Milnor, Introduction to Algebraic K-Theory. Annals of Mathematics Studies (Princeton University Press, Princeton, 1971)
R. Oliver, Whitehead Groups of Finite Groups. London Mathematical Society Lecture Note Series, vol. 132 (Cambridge University Press, Cambridge/New York, 1988)
J. Ritter, A. Weiss, On the ‘main conjecture’ of equivariant Iwasawa theory. J. Am. Math. Soc. 24, 1015–1050 (2011)
P. Schneider, O. Venjakob, K 1 of certain Iwasawa algebras, after Kakde, This volume
J.-P. Serre, Linear Representation of Finite groups. Graduate Texts in Mathematics (Springer, New York, 1977)
R. G. Swan, Algebraic K-Theory. Lecture Notes in Mathematics, vol. 76 (Springer, Berlin/New York, 1968)
O. Venjakob, On the structure theory of the Iwasawa algebra of a p-adic Lie group. J. Eur. Math. Soc. 4, 271–311 (2002)
O. Venjakob, On the work of Ritter and Weiss in comparison with Kakde’s approach, This volume
C.T.C. Wall, Norms of units in group rings. Proc. Lond. Math. Soc. 29, 593–632 (1974)
C. Weibel, The K-book: an introduction to algebraic K-theory, Available at http://www.math.rutgers.edu/~weibel/Kbook.html
A. Wiles, The Iwasawa conjecture for totally real fields. Ann. Math. 131, 493–540 (1990)
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Sujatha, R. (2013). Reductions of the Main Conjecture. In: Coates, J., Schneider, P., Sujatha, R., Venjakob, O. (eds) Noncommutative Iwasawa Main Conjectures over Totally Real Fields. Springer Proceedings in Mathematics & Statistics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32199-3_2
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