Recent papers of David Harbater

(2011-present)

The local lifting problem for actions of finite groups on curves (with 
   T. Chinburg and R. Guralnick).  Annales scientifiques de l'ENS, 
   vol. 44, no. 4 (2011), 537-605.
   pdf file of the preprint

Patching subfields of division algebras (with J. Hartmann and D. Krashen).  
   Transactions of the AMS, vol. 363, no. 6 (2011), 3335-3349.
   pdf file of the preprint

Embedding problems and open subgroups (with K. Stevenson).
   Proceedings of the AMS, vol. 139, no. 4 (2011), 1141-1154.
   pdf file of the preprint
   
Division algebras and patching (with J. Hartmann).  Lecture notes for
   the 2012 Arizona Winter School.  2012 manuscript. pdf file
   Also available at the AWS 2012 website.
   
Patching in Algebra: Notes from the Luxembourg Winter School, 
   in "Winter School on Galois Theory Volume II: Luxembourg 2012",
   Travaux mathematiques, Volume 23 (2013), 37-86, University of Luxembourg, 
   ed. by Gabor Wiese, Sara Arias-de-Reyna, and Lior Bary-Soroker.
   pdf file of the preprint
   
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
   
Weierstrass preparation and algebraic invariants (with J. Hartmann  
   and D. Krashen).  Mathematische Annalen, vol. 356, no. 4 (2013),
   1405-1424.  DOI 10.1007/s00208-012-0888-8.  Published online  
   Dec. 2012 at www.springerlink.com. 
   pdf file of the preprint

Local-global principles for Galois cohomology (with J. Hartmann 
   and D. Krashen).  Commentarii Mathematici Helvetici,
   vol. 89, no. 1 (2014), 215-253.  DOI 10.4171/CMH/317.
   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 January, 2015, at imrn.oxfordjournals.org.
   pdf file of the preprint.
   
Shreeram Abhyankar (July 22, 1930 - November 2, 2012), S. Mulay and 
   A. Sathaye, eds.  Notices of the AMS, vol. 61, no. 10, Nov. 2014, 
   1196-1216.  D. Harbater portion: 1205-1207. pdf file.  
   
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.
   
Abhyankar's conjectures in Galois theory: Current status and future directions
   (with A. Obus, R. Pries, and K. Stevenson).  Bulletin of the AMS.
   Article electronically published on October 23, 2017.
   pdf file of the preprint. 
   
 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.
   
Differential embedding problems over complex function fields
   (with A. Bachmayr, J. Hartmann, and M. Wibmer).  2016 manuscript, 
   to appear in Documenta Mathematica.
   pdf file of the preprint.
   
Differential Embedding Problems over Laurent series fields
   (with A. Bachmayr and J. Hartmann).  2017 manuscript.
   pdf file of the preprint.
   
Large Fields in Differential Galois Theory
   (with A. Bachmayr, J. Hartmann, and Florian Pop).  2017 manuscript.
   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, V. Suresh).
   2017 manuscript. pdf file of the preprint.
   
Local-global Galois theory of arithmetic function fields
   (with J. Hartmann, D. Krashen, R. Parimala, V. Suresh).  
   2017 manuscript.  pdf file of the preprint.       
   
   
       

Earlier papers.

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