Author | Snaith, Victor P. author |
---|---|
Title | Algebraic K-Groups as Galois Modules [electronic resource] / by Victor P. Snaith |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8207-1 |
Descript | X, 309 p. online resource |
1 Galois Actions and L-values -- 1.1 Analytic prerequisites -- 1.2 The Lichtenbaum conjecture -- 1.3 Examples of Galois structure invariants -- 2 K-groups and Class-groups -- 2.1 Low-dimensional algebraic K-theory -- 2.2 Perfect complexes -- 2.3 Nearly perfect complexes -- 2.4 Higher-dimensional algebraic K-theory -- 2.5 Describing the class-group by representations -- 3 Higher K-theory of Local Fields -- 3.1 Local fundamental classes and K-groups -- 3.2 The higher K-theory invariants ?s(L/K,2) -- 3.3 Two-dimensional thoughts -- 4 Positive Characteristic -- 4.1 ?1(L/K,2) in the tame case -- 4.2 $$ Ext_{Z[G(L/K)]}̂2(F_{{v̂d}}̂*,F_{{v̂{2d}}}̂*) $$ -- 4.3 Connections with motivic complexes -- 5 Higher K-theory of Algebraic Integers -- 5.1 Positive รฉtale cohomology -- 5.2 The invariant ?n(N/K,3) -- 5.3 A closer look at ?1(L/K,3) -- 5.4 Comparing the two definitions -- 5.5 Some calculations -- 5.6 Lifted Galois invariants -- 6 The Wiles unit -- 6.1 The Iwasawa polynomial -- 6.2 p-adic L-functions -- 6.3 Determinants and the Wiles unit -- 6.4 Modular forms with coefficients in ?[G] -- 7 Annihilators -- 7.1K0(Z[G], Q) and annihilator relations -- 7.2 Conjectures of Brumer, Coates and Sinnott -- 7.3 The radical of the Stickelberger ideal