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Brauer group and its arithmetic for curves over local fields.

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Abstract:

The Brauer group is an arithmetic invariant associated with a field that classifies all finite-dimensional central division algebras over the given field. In this talk, we will start by providing some motivation and the definition of the Brauer group of fields. We will then extend this definition to more general objects such as algebraic varieties. For varieties of dimension one (referred to as "curves"), the Brauer group is closely connected to their Picard group. We will explore this connection in this talk and present some new results on this topic, which are part of a joint work with Amalendu Krishna and Samiron Sadhukhan.

About the speaker:

He is a mathematician who works in the fields of algebraic K-theory and arithmetic geometry. Specifically, he is interested in problems related to class field theory for varieties, Chow groups of zero cycles, and the Brauer group of varieties.

Since June 2023, he has been a postdoctoral fellow at the Harish-Chandra Research Institute, Prayagraj. From 2017 to 2023, he pursued his PhD at the Tata Institute of Fundamental Research (TIFR), Mumbai.

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