Hermitian K -theory and 2-regularity for totally real number fields
Identifieur interne : 000089 ( Main/Exploration ); précédent : 000088; suivant : 000090Hermitian K -theory and 2-regularity for totally real number fields
Auteurs : A. Jon Berrick [Singapour] ; Max Karoubi [France] ; Paul Arne Stv R [Norvège]Source :
- Mathematische Annalen [ 0025-5831 ] ; 2011-01-01.
Abstract
Abstract: 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.
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DOI: 10.1007/s00208-010-0503-9
Affiliations:
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Ann.</title><idno type="ISSN">0025-5831</idno><idno type="eISSN">1432-1807</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2011-01-01">2011-01-01</date><biblScope unit="volume">349</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="117">117</biblScope><biblScope unit="page" to="159">159</biblScope></imprint><idno type="ISSN">0025-5831</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5831</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: 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.</div></front></TEI><affiliations><list><country><li>France</li><li>Norvège</li><li>Singapour</li></country><region><li>Île-de-France</li><li>Østlandet</li></region><settlement><li>Oslo</li><li>Paris</li></settlement><orgName><li>Université nationale de Singapour</li></orgName></list><tree><country name="Singapour"><noRegion><name sortKey="Berrick, A Jon" sort="Berrick, A Jon" uniqKey="Berrick A" first="A. Jon" last="Berrick">A. 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