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Bounds For Étale Capitulation Kernels II

Mohsen Asghari-Larimi, Abbas Movahhedi (2009)

Annales mathématiques Blaise Pascal

Let p be an odd prime and E / F a cyclic p -extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale K -groups of the ring of S -integers of E / F , where S is a finite set of primes containing those which are p -adic.

Karoubi’s relative Chern character and Beilinson’s regulator

Georg Tamme (2012)

Annales scientifiques de l'École Normale Supérieure

We construct a variant of Karoubi’s relative Chern character for smooth varieties over 𝐂 and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.

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...

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