Two-primary algebraic K-theory of two-regular number fields
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Cites background or methods from "Two-primary algebraic K-theory of t..."
...We can then improve on this result by invoking work of Rognes–Østvær [18] who in turn heavily use Voevodsky’s celebrated result, the proof of the Milnor Conjecture [22], which implies in the cases at hand that the 2-part in both groups is trivial, and a result of Weibel [25, Theorem 70, Example 75] which relies on another deep result by Rost and Voevodsky (formerly the Bloch-Kato Conjecture, see [23] and, e.g., a recent Bourbaki talk by J. Riou [16]) to show that p = 3 does not divide the order of K4 ( Z[(1 + √ −3)/2])....
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...Rognes and Østvær [18] show that the group K2n(R) has trivial 2-part if R is the ring of integers of a 2-regular number field F....
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...We can then improve on this result by invoking work of Rognes–Østvær [18] who in turn heavily use Voevodsky’s celebrated result, the proof of the Milnor Conjecture [22], which implies in the cases at hand that the 2-part in both groups is trivial, and a result of Weibel [25, Theorem 70, Example 75] which relies on another deep result by Rost and Voevodsky (formerly the Bloch-Kato Conjecture, see [23] and, e....
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2 citations
Cites methods from "Two-primary algebraic K-theory of t..."
...Our proof of the first theorem is based on the techniques employed in the case of the rational numbers [4] 1 and the analogous algebraic K-theoretic result established in [15], [24] and [26] (see Appendix A for an overview)....
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References
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"Two-primary algebraic K-theory of t..." refers background in this paper
...A number field F is called2-regular [ GJ ] if the 2-Sylow subgroup R2(F) of the kernel in K2(F) of the regular symbols attached to the non-complex places of F , is trivial....
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