Download The Conference on L-functions: Fukuoka, Japan, 18-23 by Lin Weng, Masanobu Kaneko PDF

By Lin Weng, Masanobu Kaneko

This important quantity collects papers written via a few of the world's best specialists on L-functions. It not just covers a variety of themes from algebraic and analytic quantity theories, automorphic kinds, to geometry and mathematical physics, but in addition treats the idea as a complete. The contributions replicate the newest, so much complicated and most vital facets of L-functions. particularly, it comprises Hida's lecture notes on the convention and on the Eigen style semester in Harvard collage and Weng's precise account of his works on excessive rank zeta features and non-abelian L-functions.

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Additional resources for The Conference on L-functions: Fukuoka, Japan, 18-23 February 2006

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Katz, p-adic L-functions for CM fields, Inventiones Math. 49 (1978), 199-297. [Ki] M. Kisin, Overconvergent modular forms and the Fontainemazur conjecture, Inventiones Math. 153 (2003), 373^4-54. [Kil] M. Kisin, Geometric deformations of modular Galois representations, Inventiones Math. 157 (2004), 275-328. [Ki2] M. Kisin, Moduli of finite flat group schemes, and modularity, preprint, 2005. [MTT] B. Mazur, J. Tate and J. Teitelbaum, On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Inventiones Math.

Then 1. Se\F(Ad(p) ®w W*) isfinitefor any p e ®k(W) and R = K[[Xv]]pelp ifi<2,v ~ K\,P ^ I far all p 6 JLP, 2. "RF is a reduced local complete intersection free of finite rank over W[[TF]], 3. Se\*F(Ad(gF) <&RFftp)is a torsion Hf-module, 4. For an irreducible component Spf (I) of Spf("RF), write pi = n o gF for the projection n : "RF -» I- Then Se\*F(Ad(pi) ®i I*) is a torsion l-module. Proof. If R is reduced and free of finite rank over W, QR/W is a finite module. Thus the first assertion follows.

If further we insist on <%(W[[TV]]) = 0, since WflTV]]-algebra structure is given by 6pa~x which is the character of lower right corner of g (restricted to / p ) this means the corresponding cocycle u\if has values in {(oo)}- Since Tr(u) = 0, we conclude u\Ip e T^Ad{X). If L is finite, we may tale X = L, and this gives the desired isomorphism, because T <8>A A* = Ad(L). If L is not finite, then L <2>A A* can be written as a union of Ad(X) for finite X, and by taking the inductive limit, we get the assertion.

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