অর্ণব কুণ্ডু

Preprints

• Beilinson-Lichtenbaum phenomenon for motivic cohomology (with Tess Bouis), submitted, 2025.

  We show that motivic cohomology recovers algebraic cycles. We also prove a purity result over deeply-ramified bases. The latter could provide a cohomological refinement of an ingredient in Nizioł's proof of the crystalline conjecture.

• Isotropic torsors on smooth algebras over Prüfer rings, submitted, 2025.

  We demonstrate that a generically trivial torsor under a totally isotropic reductive group scheme on a smooth algebra over a valuation ring of rank one is trivial. This generalises the results of my thesis, which proved the same in the case of quasi-split groups.

• Gersten's injectivity for smooth algebras over valuation rings, submitted, 2024.

  We prove that the K-groups of the local rings of smooth algebras over valuation rings inject inside the K-groups of their fraction fields.

Publications

• Tilting correspondences of perfectoid rings, J. Ramanujan Math. Soc. 38, No. 1 (2023) 23–32, journal.

  We establish Scholze's tilting equivalences of étale cohomology of perfectoid rings algebraically without using tools from almost ring theory or adic spaces.

Thesis

• Torsors on Smooth Algebras over Valuation Rings, CNRS-HAL Id : tel-04129990 (2023).

  We demonstrate that a generically trivial torsor under a quasi-split reductive group scheme on a smooth algebra over a valuation ring of rank one is trivial.