A gentle course in class field theory

Lecturer: Dongsheng Wu (吴冬生, Assistant Professor in Practice)

Time: Mon, Wed 10:40-12:15

Venue: A1-103

Zoom: 462 110 5973

Password: BIMSA

Introduction

类域论是20世纪上半叶代数数论的重大成果，其主题是利用一个域的算术信息来刻画该域的所有Abel扩域。类域论在诸多数学领域都有广泛应用和深刻影响。数学家Weil甚至认为每个数学家都应该掌握类域论，正如每个数学家都应该掌握Galois理论一样。

类域论有多种证明途径。本课程将采用理想群的同余子群这一途径。该途径所需的预备知识最少，也最便于一般数学工作者的理解和应用。

Reference

J. W. S. Cassels and A. Fröhlich, editors. “Algebraic Number Theory”, Thompson Publ. Washington, D. C., 1967

N. Childress, “Class Field Theory”, Springer, New York, 2009

P. Guillot, “A gentle Course in Local Class Field Theory”, Cambridge University Press, 2018

G. J. Janusz, “Algebraic Number Fields”, Academic Press, New York and London, 1973

S. Lang, “Algebraic Number Theory”, Springer-Verlag, 1994

J. Neukirch, “Algebraic Number Theory”, Springer-Verlag, Berlin, 1999