Rankeya Datta
Department of Mathematics, Statistics and Computer Science
University of Illinois Chicago
Email: rankeya(at)uic(dot)edu
Office: SEO 411
I am a Research Assistant Professor in the Mathematics Department at University of Illinois Chicago. I recently completed my Ph.D. from the University of Michigan, where I was advised by Karen Smith.
I work at the interface of algebraic geometry and commutative algebra, specializing in the use of local prime characteristic methods (in commutative algebra) and their global variants. I often enjoy thinking about nonNoetherian objects such as valuation rings, perfectoid rings, and more recently, rings of differential operators.
Teaching
Winter 2019: Math 210 (the course website). Here is the website for my sections.
Papers
 On some permanence properties of (derived) splinters (joint with Kevin Tucker). In preparation.
 HilbertKunz multiplicity of fibers and Bertini theorems (joint with Austyn Simpson).
 Annihilators of Dmodules in mixed characteristic (joint with Nicholas Switala and Wenliang Zhang).
 Permanence properties of Finjectivity (joint with Takumi Murayama).
 Frobenius splitting of valuation rings and Fsingularities of centers.
 Uniform approximation of Abhyankar valuation ideals in function fields of prime characteristic. To appear in Transactions of AMS.
 Excellence in Prime Characteristic (joint with Karen Smith). Contemporary Mathematics, Local and Global Methods in Algebraic Geometry, 712
(2018), 105116.
 (Non)Vanishing results on local cohomology of valuation rings. Journal of Algebra 4791(2017), 413436. DOI 10.1016/j.jalgebra.2016.12.03.
 Frobenius and valuation rings (joint with Karen Smith). Algebra & Number Theory 105 (2016), 10571090. DOI 10.2140/ant.2016.10.1057; corrigendum: Correction to the article Frobenius and valuation rings. Algebra & Number Theory 114 (2017), 10031007. DOI 10.2140/ant.2017.11.1003.
 Free and very free morphisms on a Fermat hypersurface (joint with T. Bridges, J. Eddy, M. Newman, J. Yu). Involve 6 (2013), No. 4, 437445.
 Polygons in quadratically closed rings and properties of nadically closed rings (undergraduate thesis supervised by Aise Johan de Jong).
Thesis
Here is a copy of my dissertation. Corrections are welcome!
Notes
Notes are subject to change without notice.
 Very rough notes (prepared for a Grad seminar at UMich) on a proof of a theorem of Kunz, characterizing regularity of Noetherian rings in terms of flatness of Frobenius, using the surprising homological properties of perfect rings. Based loosely on a talk given by Bhatt at Gennady Lyubeznik's 60th birthday conference, the notes are a more verbose version of the original proof appearing in a paper by BhattScholze.
 Notes on Huber rings for a learning seminar at the University of Michigan (Winter 2017). Last updated Feb 18, 2017. A new section was added on uniform Huber rings (not discussed in the lectures), following Bhargavâ€™s discussion of uniform KBanach algebras in his course. In particular, we prove equivalence of categories results generalizing [Bha17, Thm 9.7 and Cor 9.9].
 On a vanishing result in sheaf cohomology. An example is given of a nonquasicompact scheme that violates a vanishing result in sheaf cohomology that holds for certain quasicompact spaces [Stacks Project, Tag02UX]. This example can be interpreted purely topologically (without mentioning schemes), and is incorporated in the latter form in Tag0BX0.
 Notes from a summer minicourse I taught at Michigan on notions of singularities in prime characteristic in 2016. The notes have not been proofread and do not cover a lot of material.
