Preprints:

  1. Elliptic curves and their principal homogeneous spaces: splitting Severi—Brauer varieties
    (joint with Nick Rekuski)
    [Preprint. 24 Pages. January 18, 2024]

  2. On the algebraizability of formal deformations in $K$-cohomology
    [Preprint. 17 Pages. March 27, 2024]
    (Older version. 36 Pages. December 7, 2023)

  3. The period and index of a generic geometrically elliptic normal curve
    [Preprint. 18 Pages. December 3, 2023]
    (Previous version. 32 Pages. December 2, 2023)

Publications:

  1. Pro-representability of $K^M$-cohomology in weight 3 generalizing a result of Bloch
    To appear in Annals of K-theory
    [Final Preprint. 13 pages. January 19, 2023]

  2. On the Chow groups of a biquaternion Severi—Brauer variety
    To appear in Pacific Journal of Mathematics
    [Final preprint. 16 Pages. October 17, 2022]
    {Slides from a talk on this paper. 19 MB}

  3. Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior
    Documenta Mathematica. Vol. 26 (2021), 523—536.
    [Final Preprint. 14 Pages. April 23, 2021]

  4. A universal coefficient theorem with applications to torsion in Chow groups of Severi--Brauer varieties
    New York Journal of Mathematics. Vol. 26 (2020), 1155—1183.
    [Final Preprint. 25 Pages. April 29, 2020]
    {Slides from a talk on this paper. 7MB}

  5. Codimension 2 cycles on Severi-Brauer varieties and decomposability
    Manuscripta Mathematica. Vol. 165 (2021), No. 3-4, 521—536.
    [Final Preprint. 13 Pages. June 23, 2020]
    (Corrections. 1 Page. October 14, 2020)

  6. $\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead
    Homology, Homotopy and Applications. Vol. 23 (2021), No. 1, 257—274.
    [Final Preprint. 15 Pages. July 2, 2020]
    {Slides from a talk on this paper. 9MB}

  7. Universal additive Chern classes and a GRR-type theorem
    Journal of Algebra. Vol. 560 (2020), 1173—1189.
    [Final Preprint. 14 Pages. June 4, 2020]

  8. Functorality of the gamma filtration and computations for some twisted flag varieties
    Annals of K-theory. Vol. 5 (2020), No. 1, 159—180.
    [Final Preprint. 16 Pages. August 21, 2019]

  9. On the K-theory coniveau epimorphism for products of Severi-Brauer varieties
    (joint with Nikita Karpenko) 
    Annals of K-theory. Vol. 4 (2019), No. 2, 317—344.
    [Final Preprint. 21 Pages. October 19, 2018]

  10. The coniveau filtration on $\mathrm{K}_1$ for some Severi-Brauer varieties
    Canadian Mathematical Bulletin Vol. 62 (2019), No. 3, 565—576.
    [Final Preprint. 11 Pages. October 9, 2018]

notEs:

  1. Rational equivalence of curves on a Severi—Brauer variety
    [Unpublished. 10 Pages. July 16, 2021]

  2. The arithmetic genus of a complete intersection curve
    [Unpublished. 4 Pages. May 11, 2020] (BibTex)

  3. The genera of smooth curves in a projective variety
    [Unpublished. 6 Pages. December 12, 2019] (BibTex)

  4. A degree-bound on the genus of a projective curve
    [Unpublished. 4 Pages. October 3, 2021] (BibTex)