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Number Theory Seminar

Title: Class field theory for varieties over local fields
Speaker: Jitendra Rathore (TIFR Mumbai)
Date: 20 April 2023
Time: 11 AM
Venue: LH-1

The (tame) class field theory for a smooth variety $X$ is the study of describing the abelianized (tame) {'e}tale fundamental group of $X$in terms of some groups which are defined using algebraic cycles of $X$. In this talk, we study the tame class field theory for smooth varieties over local fields. We will begin with defining few notions and recalling various results from the past to overview the historical background of the subject. We will then study abelianized tame fundamental group denoted as $\pi^{ab,t}_{1}(X)$, with the help of reciprocity map $\rho^{t}_{X} : C^{t}(X) \rightarrow \pi^{ab,t}_{1}(X)$ and will describe the kernel and topological cokernel of this map. This talk is based on a joint work with Prof. Amalendu Krishna and Dr. Rahul Gupta.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 31 May 2023