Research Interest: My mathematical research interests lie in the fields of algebraic K-theory, arithmetic geometry, algebraic geometry, and geometric class field theory. Specifically, I like to think about problems related to various algebraic and arithmetic invariants, such as étale fundamental groups, algebraic K-groups, Brauer groups, Chow groups, motivic cohomology groups, Milnor K-groups, and étale cohomology groups. I also like to explore the relations among these invariants. These invariants are associated with a field or, more generally, with an algebraic variety and contain significant arithmetic information about the variety.
Keywords: Algebraic K-groups, Brauer group, Milnor K-groups, Galois cohomology, Chow groups, Motivic cohomology groups, etale cohomology groups, tame fundamental groups, etc.
Research Papers:
(with R. Gupta and A. Krishna) A Decomposition theorem for 0-cycles and applications, Ann. Sc. Norm. Super. Pisa Cl. Sci (5) 25 (2024) p. 449-482. Journal Arxiv
(with A. Krishna and S. Sadhukhan) Duality theorems for curves over local fields , Trans. Amer. Math. Soc. Ser. B 11 (2024), 945-1014. Journal Arxiv
(with R. Gupta and A. Krishna) Tame Class Field theory over local fields (Submitted, Arxiv ).
(with R. Gupta) Torsion in abelian fundamental group and its application (Submitted, Arxiv ).
(with E. Gazaki) Zero-cycles on quasi-projective surfaces over p-adic fields (Submitted, Arxiv).