Research output: Chapter in Book/Report/Conference proceeding › Conference paper

Original language | English |
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Title of host publication | Elliptic Curves, Modular Forms and Iwasawa Theory |

Editors | David Loeffler, Sarah Zerbes |

Publisher | Springer |

Pages | 295-309 |

Number of pages | 15 |

Volume | 188 |

ISBN (Electronic) | 9783319450322 |

ISBN (Print) | 9783319450315 |

DOIs | |

E-pub ahead of print | 16 Jan 2017 |

Additional links | |

Event | Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 - Cambridge, United Kingdom Duration: 25 Mar 2015 → 27 Mar 2015 |

Name | Springer Proceedings in Mathematics & Statistics |
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Publisher | Springer |

Volume | 188 |

Conference | Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 |
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Country | United Kingdom |

City | Cambridge |

Period | 25/03/2015 → 27/03/2015 |

Let p be an odd prime and let G be a p-adic Lie group. The group K1(Λ(G)), for the Iwasawa algebra Λ(G), is well understood in terms of congru- ences between elements of Iwasawa algebras of abelian sub-quotients of G due to the work of Ritter-Weiss and Kato (generalised by the author). In the former one needs to work with all abelian subquotients of G whereas in Kato’s approach one can work with a certain well-chosen sub-class of abelian sub-quotients of G. For instance in [11] K1(Λ(G)) was computed for meta-abelian pro-p groups G but the congruences in this description could only be proved for p-adic L-functions of totally real fields for certain special meta-abelian pro-p groups. By changing the class of abelian subquotients a different description of K1(Λ(G)), for a general G, was obtained in [12] and these congruences were proven for p-adic L-functions of totally real fields in all cases. In this note we propose a strategy to get an alternate description of K1(Λ(G)) when G = GL2(Zp). For this it is sufficient to compute K1 (Zp [GL2 (Z/pn )]). We demonstrate how the strategy should work by explicitly computing K1(Zp[GL1(Z/p)])(p), the pro-p part of K1(Zp[GL2(Z/p)]), which is the most interesting part.

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