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Registration:
10:00-12:00, 13:30-15:30, August 2 - 4, 2016
10:00-12:00, 13:30-15:50, August 9 - 11, 2016
Room 734, 4th Floor, The 3rd General Building, NTHU
Organizers:
Chieh-Yu Chang ( National Tsing Hua University )
Fu-Tsun Wei ( National Central University )
Speakers:
(1) Prof. Chieh-Yu Chang (NTHU),
(2) Prof. Fu-Tsun Wei (NCU)
Topic I: Local class field theory
-Formal groups
-Constructions of maximal abelian extensions of p-adic local fields
-The reciprocity map and the existence theorem
Topic II: Tate’s thesis
-Characters and measures
-Local zeta-functions and functional equations
-Analytic continuation and functional equation of the global zeta-function
-Comparison with class field theory
Abstract:
We will introduce Fourier analysis on adeles and employ a reformulation of Grossencharacters on ideles, and then give an elegant proof of Hecke’s work following Tate. Nowadays, Tate’s work is generally realized as study of automorphic forms for GL(1). This short course provides a thorough treatment following Tate’s approaches. Before introducing Tate’s work, we need to introduce some background on class field theory. We will give more details on local class field theory, and then give the structural theorems on global class field theory. Finally we will give the connection between them.
References:
1. Jonathan Lubin and John Tate, Formal complex multiplication in local fields. Ann. of Math. (2) 81 1965 380–387.
2. Dinakar Ramakrishnan and Robert J. Valenza, Fourier analysis on number fields, GTM 186
3. J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, LMS
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