Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bley, Werner and Cobbe, Alessandro 2016. Equivariant epsilon constant conjectures for weakly ramified extensions. Mathematische Zeitschrift, Vol. 283, Issue. 3-4, p. 1217.


    BUCKINGHAM, PAUL 2014. THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS. Glasgow Mathematical Journal, Vol. 56, Issue. 02, p. 335.


    Macias Castillo, Daniel 2013. On higher order Stickelberger-type theorems. Journal of Number Theory, Vol. 133, Issue. 9, p. 3007.


    MACIAS CASTILLO, DANIEL 2012. ON HIGHER-ORDER STICKELBERGER-TYPE THEOREMS FOR MULTI-QUADRATIC EXTENSIONS. International Journal of Number Theory, Vol. 08, Issue. 01, p. 95.


    Nickel, Andreas 2011. On the equivariant Tamagawa number conjecture in tame CM-extensions, II. Compositio Mathematica, Vol. 147, Issue. 04, p. 1179.


    Nickel, Andreas 2011. On the equivariant Tamagawa number conjecture in tame CM-extensions. Mathematische Zeitschrift, Vol. 268, Issue. 1-2, p. 1.


    Nickel, Andreas 2010. Non-commutative Fitting invariants and annihilation of class groups. Journal of Algebra, Vol. 323, Issue. 10, p. 2756.


    Bley, Werner and Wilson, Stephen M. J. 2009. Computations in Relative Algebraic K-Groups. LMS Journal of Computation and Mathematics, Vol. 12, p. 166.


    Kim, Sey 2006. On congruence relations between the fundamental units of biquadratic fields. Journal of Number Theory, Vol. 121, Issue. 1, p. 7.


    Burns, David Köck, Bernhard and Snaith, Victor 2004. Refined and l-adic Euler characteristics of nearly perfect complexes. Journal of Algebra, Vol. 272, Issue. 1, p. 247.


    Jehanne, Arnaud Roblot, Xavier-Francois and Sands, Jonathan 2003. Numerical Verification of the Stark-Chinburg Conjecture for Some Icosahedral Representations. Experimental Mathematics, Vol. 12, Issue. 4, p. 419.


    ×

Equivariant Tamagawa Numbers and Galois Module Theory I

  • D. Burns (a1)
  • DOI: http://dx.doi.org/10.1023/A:1014502826745
  • Published online: 01 November 2001
Abstract

Let L/K be a finite Galois extension of number fields. We use complexes arising from the étale cohomology of $\Bbb Z$ on open subschemes of Spec $\cal O$L to define a canonical element of the relative algebraic K-group K0($\Bbb Z$[Gal(L/K)], $\Bbb R$. We establish some basic properties of this element, and then use it to reinterpret and refine conjectures of Stark, of Chinburg and of Gruenberg, Ritter and Weiss. Our results precisely explain the connection between these conjectures and the seminal work of Bloch and Kato concerning Tamagawa numbers. This provides significant new insight into these important conjectures and also allows one to use powerful techniques from arithmetic algebraic geometry to obtain new evidence in their favour.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Equivariant Tamagawa Numbers and Galois Module Theory I
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Equivariant Tamagawa Numbers and Galois Module Theory I
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Equivariant Tamagawa Numbers and Galois Module Theory I
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: