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Area preserving pl homeomorphisms and relations in K 2

Peter Greenberg (1998)

Annales de l'institut Fourier

To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in K 2 of the smallest field whose elements are needed to write the homeomorphism.Using a formula of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a “reciprocity” formula for a pair of triangles in the plane, and some explicit elements of torsion in K 2 of certain function fields are found.

Cohomologie des algèbres de Lie croisées et K -théorie de Milnor additive

Daniel Guin (1995)

Annales de l'institut Fourier

Dans cet article, nous définissons des modules de (co)-homologie 0 ( 𝔊 , 𝔄 ) , 1 ( 𝔊 , 𝔄 ) , ( 𝔊 , 𝔄 ) , 1 ( 𝔊 , 𝔄 ) 𝔊 et 𝔄 sont des algèbres de Lie munies d’une structure supplémentaire (algèbres de Lie croisées), qui satisfont les propriétés usuelles des foncteurs cohomologiques. Si A est une k -algèbre, nous utilisons ces modules d’homologie pour comparer le groupe d’homologie cyclique H C 1 ( A ) avec un analogue additif du groupe de K -théorie de Milnor K 2 Madd ( A ) .

Formules explicites pour le caractère de Chern en K -théorie algébrique

Grégory Ginot (2004)

Annales de l'Institut Fourier

Dans cet article on donne une formule explicite pour le caractère de Chern reliant la K - théorie algébrique et l’homologie cyclique négative. On calcule le caractère de Chern des symboles de Steinberg et de Loday et on donne une preuve élémentaire du fait que le caractère de Chern est multiplicatif.

On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields

P. E. Conner, J. Hurrelbrink (1995)

Acta Arithmetica

A large number of papers have contributed to determining the structure of the tame kernel K F of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for K F have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms,...

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K E . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form ( ( p . . . p k ) ) , where the primes p i are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of K E is zero for such fields. In the course of proving...

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