Homological Methods in Number Theory | Amit Kumar Basistha | B.Math, 2022-25

Title: Homological Methods in Number Theory

Speaker: Amit Kumar Basistha (B. Math, 3rd year)

Abstract: The application of Homological Methods in Algebraic Number Theory, particularly in Class Field Theory, gained popularity around the 1950s and has propelled enormous advancement in the subject. In this talk, I will introduce some notions of Group Cohomology and how they are applicable in Number Theory. In particular, I will introduce the notion of 'Abstract Class Formation' and define the reciprocity isomorphism and its functorial properties. Finally I will present a nice characterization of the Norm Groups of a Local Field.

Prerequisites: Knowledge of Abstract Algebra and some point set topology will be assumed. Further the content of the talk on Homological Algebra by Sankha Subhra Chakraborty will be assumed.