Local-global principles for torsors over arithmetic curves (with
J. Hartmann and D. Krashen). American Journal of Mathematics,
vol. 137, no. 6 (2015), 1559-1612.
pdf file of the preprint
Refinements to patching and applications to field invariants
(with J. Hartmann and D. Krashen). International Mathematics
Research Notices, 2015, 10399-10450; doi: 10.1093/imrn/rnu278.
Published online at imrn.oxfordjournals.org.
pdf file of the preprint.
Riemann's Existence Theorem. In "The Legacy of Bernhard Riemann After
150 Years" (ed. by L. Ji, F. Oort, S.-T. Yau), Higher Education Press
and International Press, Beijing-Boston, 2015, pp. 275-286.
pdf file of the preprint.
Differential Galois groups over Laurent series fields (with
A. Bachmayr and J. Hartmann). Proceedings of the London
Mathematical Society, vol. 112, no. 3 (2016), 455-476.
pdf file of the preprint. Published version.
Global Oort Groups (with T. Chinburg and R. Guralnick). Journal of Algebra,
vol. 473 (2017), 374-396. pdf file of the preprint.
Link to published version at Science Direct.
Abhyankar's conjectures in Galois theory: Current status and future directions
(with A. Obus, R. Pries, and K. Stevenson). Electronic publication.
Bulletin of the AMS, vol. 55, no. 2, April 2018, 239-287.
pdf file of the preprint.
Differential embedding problems over complex function fields
(with A. Bachmayr, J. Hartmann, and M. Wibmer).
Documenta Mathematica, vol. 23 (2018), 241-291.
pdf file of the preprint.
Differential embedding problems over Laurent series fields
(with A. Bachmayr and J. Hartmann).
Journal of Algebra, vol. 513 (2018), 99-112.
DOI: 10.1016/j.jalgebra.2018.07.017. pdf file of the preprint.
Local-Global Principles for Zero-Cycles on Homogeneous Spaces over
Arithmetic Function Fields (with J.-L. Colliot-Thélène,
J. Hartmann, D. Krashen, R. Parimala, and V. Suresh).
Transactions of the AMS, vol. 372 (2019), no. 8, 5263-5286.
DOI: 10.1090/tran/7911 pdf file of the preprint.
Local-global Galois theory of arithmetic function fields
(with J. Hartmann, D. Krashen, R. Parimala, and V. Suresh).
Israel Journal of Mathematics, vol. 232, no. 2 (2019), 849-882.
pdf file of the preprint. Published version.
Local-global principles for tori over arithmetic curves (with
J.-L. Colliot-Thélène, J. Hartmann, D. Krashen, R. Parimala, and V. Suresh).
Algebraic Geometry, vol. 7 (5) (2020) 607-633; doi:10.14231/AG-2020-022.
pdf file of the preprint. Published version.
Large Fields in Differential Galois Theory
(with A. Bachmayr, J. Hartmann, and F. Pop).
J. Inst. of Math. of Jussieu, vol. 20, no. 6 (2021), 1931-1946;
doi:10.1017/S1474748020000018.
Online publication. pdf file of the preprint.
Local-global principles for curves over semi-global fields (with D. Krashen and
Alena Pirutka). Bulletin of the London Math. Society,
vol. 53, issue 1 (2021) 177-193. Online publication;
doi:10.1112/blms.12409. pdf file of the preprint.
A comparison between obstructions to local-global principles over
semi-global fields (with J. Hartmann, V. Karemaker, F. Pop).
In: Abelian Varieties and Number Theory (M. Jarden and T. Shaska, eds.),
pp. 135-146, Contemp. Mathematics, vol. 767, AMS, 2021.
pdf file of the preprint.
Free differential Galois groups
(with A. Bachmayr, J. Hartmann, and M. Wibmer).
Transactions of the AMS, vol. 374, no. 6 (2021), 4293-4308.
pdf file of the preprint. Link to the published version.
Pre-Galois theory (with P. Dèbes).
Osaka Journal of Math., vol. 58 (2021), 71-101.
pdf file of the preprint.
Available at Project Euclid.
The differential Galois group of the rational function field
(with A. Bachmayr, J. Hartmann, and M. Wibmer).
Advances in Mathematics, vol. 381 (2021), 107605, 1-27.
Published version. pdf file of the preprint.
Adelic double cosets over semi-global fields.
Albanian Journal of Math., vol. 15, no. 2 (2021), 99-115.
pdf file of the preprint.
Local-global principles for constant reductive groups over semi-global fields
(with J.-L. Colliot-Thélène, J. Hartmann, D. Krashen, R. Parimala, and
V. Suresh). Michigan Math. J. vol. 72 (2022), 77-144.
pdf file of the preprint.
Bounding cohomology classes over semiglobal fields
(with J. Hartmann and D. Krashen).
Israel Journal of Mathematics, vol. 257 (2023), 353-387.
pdf file of the preprint. Link to the published version.
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