Preprints:
Elliptic curves and their principal homogeneous spaces: splitting Severi—Brauer varieties
(joint with Nick Rekuski)
[Preprint. 24 Pages. January 18, 2024]On the algebraizability of formal deformations in $K$-cohomology
[Preprint. 17 Pages. September 1, 2024]
(Older version. 36 Pages. December 7, 2023)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:
Pro-representability of $K^M$-cohomology in weight 3 generalizing a result of Bloch
Annals of K-theory. Vol. 8 (2023), No. 1, 127—139.
[Final Preprint. 13 pages. January 19, 2023]On the Chow groups of a biquaternion Severi—Brauer variety
Pacific Journal of Mathematics. Vol. 321 (2022), No. 2, 359—374.
[Final preprint. 16 Pages. October 17, 2022]
{Slides from a talk on this paper. 19 MB}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]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}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)$\mathbb{A}^1$-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}Universal additive Chern classes and a GRR-type theorem
Journal of Algebra. Vol. 560 (2020), 1173—1189.
[Final Preprint. 14 Pages. June 4, 2020]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]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]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:
Rational equivalence of curves on a Severi—Brauer variety
[Unpublished. 10 Pages. July 16, 2021]The arithmetic genus of a complete intersection curve
[Unpublished. 4 Pages. May 11, 2020] (BibTex)The genera of smooth curves in a projective variety
[Unpublished. 6 Pages. December 12, 2019] (BibTex)A degree-bound on the genus of a projective curve
[Unpublished. 4 Pages. October 3, 2021] (BibTex)