CMI PhD Research Seminar
Date: Tuesday, 22 October 2024
Time: 03:00 - 04:00 PM
Venue: LH3
Class Field Theory
Harsh Vardhan Nahata
Chennai Mathematical Institute.
22-10-24

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Abstract

Let K be a global field (e.g., Q) or a local field (e.g., Q_p.) Class field theory is the study of abelian extensions E/K, i.e., (finite or infitnite) Galois extensions whose Galois group is abelian.The main point is that one is able to understand the structure and even classify these extensions in terms of an invariant of K itself. In the global case, this invariant C_K is the idele class group. In the local case, this invariant is the multiplicative group, C_K=K*. In both cases, C_K contains “all the information” about abelian extensions of K. In the following talk we state some of the main theorems of global class field theory and prove their corresponding analogues in the local case.