My mathematical research is in the area of valuation theory and its applications to algebraic geometry and number theory. A central problem in algebraic geometry is the problem of local uniformization, which is the local version of the resolution of singularities. Closely related are the deep problems of elimination of ramification and extensions of valuations to rational function fields. Valuation theoretic tools have been used extensively in the study of all these problems.

Education

1. Arpan Dutta, Extensions of valuations to rational function fields over completions, Mathematische Nachrichten (to appear).
2. Arpan Dutta, Minimal pairs, inertia degrees, ramification degrees and implicit constant fields, Communications in Algebra, DOI : https://doi.org/10.1080/00927872.2022.2078833.
3. Arpan Dutta, On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences, Journal of Pure and Applied Algebra, 226(11), 2022. DOI : https://doi.org/10.1016/j.jpaa.2022.107107.
4. Arpan Dutta, On the implicit constant fields and key polynomials for valuation algebraic extensions, Journal of Commutative Algebra (to appear).
5. Arpan Dutta, On the non-uniqueness of maximal purely wild extensions, Communications in Algebra, 50(3), 1118–1139, 2022.
6. Arpan Dutta, Minimal pairs, minimal fields and implicit constant fields, Journal of Algebra, 588, 479–514, 2021.
7. Arpan Dutta and Franz-Viktor Kuhlmann, Eliminating tame ramification : generalizations of Abhyankar’s Lemma, Pacific Journal of Mathematics, 307(1), 121–136, 2020.
8. Arpan Dutta, Generating sequences and semigroups of valuations on 2-dimensional normal local rings, Annales de la faculte des sciences de Toulouse : Mathematiques, Serie 6, Tome 29, no. 3, 619–647, 2020.