منابع مشابه
Iwasawa Theory and Motivic L-functions
We illustrate the use of Iwasawa theory in proving cases of the (equivariant) Tamagawa number conjecture.
متن کاملMotives and Motivic L-functions
This report aims to be an exposition of the theory of L-functions from the motivic point of view. The classical theory of pure motives provides a category consisting of ‘universal cohomology theories’ for smooth projective varieties defined over – for instance – number fields. Attached to every motive we can define a function which is holomorphic on a subdomain of C which at least conjecturally...
متن کاملMotives : Motivic L - functions
The exposition here follows the lecture delivered at the summer school, and hence, contains neither precision, breadth of comprehension, nor depth of insight. The goal rather is the curious one of providing a loose introduction to the excellent introductions that already exist, together with scattered parenthetical commentary. The inadequate nature of the exposition is certainly worst in the th...
متن کاملIwasawa-Tate on ζ-functions and L-functions
After a too-brief introduction to adeles and ideles, we sketch proof of analytic continuation and functional equation of Riemann’s zeta, in the modern form due independently to Iwasawa and Tate about 1950. The sketch is repeated for Dedekind zeta functions of number fields, noting some additional complications. The sketch is repeated again for Hecke’s (größencharakter) L-functions, noting furth...
متن کاملIwasawa L-Functions and the Mysterious L-Invariant
coming from the cokernels of the rst column. These are cyclic (pro-cyclic in the limit) and are generated by the image of q t. So, lim A(K t)=NA(K n;t) = ?=< (q t ; L t =K t) > where (q t ; L t =K t) is the norm residue symbol of q t for the extension L t =K t. We write Q t for the image of (q t ; L t =K t) under the isomorphism ? ! Z p induced by sending to 1. Note that although Q t is not can...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2009
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2009.v5.n1.a8