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On Bott-periodic algebraic K-theory.

Felipe Zaldívar (1994)

Publicacions Matemàtiques

Let K*(A;Z/ln) denote the mod-ln algebraic K-theory of a Z[1/l]-algebra A. Snaith ([14], [15], [16]) has studied Bott-periodic algebraic theory Ki(A;Z/ln)[1/βn], a localized version of K*(A;Z/ln) obtained by inverting a Bott element βn. For l an odd prime, Snaith has given a description of K*(A;Z/ln)[1/βn] using Adams maps between Moore spectra. These constructions are interesting, in particular for their connections with Lichtenbaum-Quillen conjecture [16].In this paper we obtain a description...

On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.

Francesc Bars (2007)

Publicacions Matemàtiques

We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois...

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 ₂ 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 ℚ ( √ ( p ₁ . . . 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 ₂ E is zero for such fields. In the course of proving...

On the cyclotomic elements in K₂ of a rational function field

Kejian Xu, Chaochao Sun, Shanjie Chi (2014)

Acta Arithmetica

If l is a prime number, the cyclotomic elements in the l-torsion of K₂(k(x)), where k(x) is the rational function field over k, are investigated. As a consequence, a conjecture of Browkin is partially confirmed.

On the structure of Milnor K -groups of certain complete discrete valuation fields

Masato Kurihara (2004)

Journal de Théorie des Nombres de Bordeaux

For a typical example of a complete discrete valuation field K of type II in the sense of [12], we determine the graded quotients gr i K 2 ( K ) for all i > 0 . In the Appendix, we describe the Milnor K -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.

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