On two-primary algebraic K-theory of quadratic number rings with focus on K₂

Crainic, Marius; Østvær, Paul Arne

doi:10.4064/aa-87-3-223-243

Cited by 2 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For n ≡ 6 (mod 8), (17) implies that −1 KQ n (R F ) ∼ = Z or Z ⊕ Z/2. On the other hand, the exact sequence (18) shows that −1 KQ n (R F ) is a subgroup of Z.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

“…Thus Q( √ p) with p ≡ 3 (mod 4) a prime number and Q( √ 2p) with p ≡ ±3 (mod 8) a prime number fail to lie in the subclass, cf. [18].…”

Section: The Finite Abelian Groupmentioning

confidence: 99%

“…For n ≡ 5 (mod 8), (18) implies that −1 KQ n (R F ) is cyclic, whence by (17) there is an isomorphism…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

“…Chasing this sequence from the left reveals that −1 KQ n (R F ) is a finite group of order 2t n . Meanwhile, the exact sequence (18) obliges this group to be cyclic.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

See 3 more Smart Citations

Hermitian K-theory and 2-regularity for totally real number fields

2010

View full text Add to dashboard Cite

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. Moreover, the 2-regular case is precisely the class of totally real number fields that have homotopy cartesian "Bökstedt square", relating the K-theory of the 2-integers to that of the fields of real and complex numbers and finite fields. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8 in the orthogonal case. In both the orthogonal and symplectic cases, we prove a 2-primary hermitian homotopy limit conjecture for these rings.

show abstract

“…For n ≡ 6 (mod 8), (17) implies that −1 KQ n (R F ) ∼ = Z or Z ⊕ Z/2. On the other hand, the exact sequence (18) shows that −1 KQ n (R F ) is a subgroup of Z.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

“…Thus Q( √ p) with p ≡ 3 (mod 4) a prime number and Q( √ 2p) with p ≡ ±3 (mod 8) a prime number fail to lie in the subclass, cf. [18].…”

Section: The Finite Abelian Groupmentioning

confidence: 99%

“…For n ≡ 5 (mod 8), (18) implies that −1 KQ n (R F ) is cyclic, whence by (17) there is an isomorphism…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

“…Chasing this sequence from the left reveals that −1 KQ n (R F ) is a finite group of order 2t n . Meanwhile, the exact sequence (18) obliges this group to be cyclic.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

See 2 more Smart Citations