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

Marius Crainic; Paul Arne Østvær

Acta Arithmetica (1999)

- Volume: 87, Issue: 3, page 223-243
- ISSN: 0065-1036

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topMarius Crainic, and Paul Arne Østvær. "On two-primary algebraic K-theory of quadratic number rings with focus on K₂." Acta Arithmetica 87.3 (1999): 223-243. <http://eudml.org/doc/207218>.

@article{MariusCrainic1999,

author = {Marius Crainic, Paul Arne Østvær},

journal = {Acta Arithmetica},

keywords = {algebraic K-groups of quadratic number rings; 2- and 4-rank formulas for Picard groups; étale cohomology; quadratic number fields; algebraic -theory; 4-rank; tame kernel; ring of integers; strict class group},

language = {eng},

number = {3},

pages = {223-243},

title = {On two-primary algebraic K-theory of quadratic number rings with focus on K₂},

url = {http://eudml.org/doc/207218},

volume = {87},

year = {1999},

}

TY - JOUR

AU - Marius Crainic

AU - Paul Arne Østvær

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

JO - Acta Arithmetica

PY - 1999

VL - 87

IS - 3

SP - 223

EP - 243

LA - eng

KW - algebraic K-groups of quadratic number rings; 2- and 4-rank formulas for Picard groups; étale cohomology; quadratic number fields; algebraic -theory; 4-rank; tame kernel; ring of integers; strict class group

UR - http://eudml.org/doc/207218

ER -

## References

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- [13] H. Qin, The 4-rank of $K\u2082{O}_{F}$ for real quadratic fields F, Acta Arith. 72 (1995), 323-333.
- [14] D. Quillen, Finite Generation of the Groups ${K}_{i}$ of Rings of Algebraic Integers, Lectures Notes in Math. 341, Springer, 1973, 179-198. Zbl0355.18018
- [15] J. Rognes and C. Weibel, Two-primary algebraic K-theory of rings of integers in number fields, preprint, 1997; http://www.math.uiuc.edu/K-theory/0220/.
- [16] J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274. Zbl0359.12011
- [17] A. Vazzana, On the 2-primary part of K₂ of rings of integers in certain quadratic number fields, Acta Arith. 80 (1997), 225-235. Zbl0868.11054
- [18] A. Vazzana, Elementary abelian 2-primary parts of K₂𝓞 and related graphs in certain quadratic number fields, Acta Arith. 81 (1997), 253-264. Zbl0905.11051

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