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  3. Non-abelian Fundamental Groups and Iwasawa Theory
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  • Publisher:
    Cambridge University Press
    Publication date:
    January 2012
    December 2011
    ISBN:
    9780511984440
    9781107648852
    DOI:
    https://doi.org/10.1017/CBO9780511984440
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.45kg, 320 Pages
    • Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (393)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (393)
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    Book description

    Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three areas gathered at the Isaac Newton Institute in Cambridge to explain the latest advances in their research and to investigate possible avenues of future investigation and collaboration. For those in attendance, the overwhelming impression was that number theory is going through a tumultuous period of theory-building and experimentation analogous to the late 19th century, when many different special reciprocity laws of abelian class field theory were formulated before knowledge of the Artin–Takagi theory. Non-abelian Fundamental Groups and Iwasawa Theory presents the state of the art in theorems, conjectures and speculations that point the way towards a new synthesis, an as-yet-undiscovered unified theory of non-abelian arithmetic geometry.

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