Publications of Julia Hartmann

Papers

• Bounding cohomology classes over semiglobal fields. With With D. Harbater and D. Krashen. 2022 manuscript. Available at: arXiv:2203.06770.

• Local-global principles for constant reductive groups over semi-global fields. With With J.-L. Colliot-Thélène, D. Harbater, D. Krashen, R. Parimala and V. Suresh. 2021 manuscript. Accepted for publication in MMJ. Available at: arXiv:2108.12349.

• The differential Galois group of the rational function field. With A. Bachmayr , D. Harbater and M. Wibmer. Advances in Mathematics 381 (2021), Paper No. 107605.

• A comparison between obstructions to local-global principles over semi-global fields. With D. Harbater, V. Karemaker and F. Pop. In: Abelian Varieties and Number Theory, Contemp. Mathematics 767, 135-146, AMS, 2021, Eds. M. Jarden, T. Shaska.

• Large Fields in Differential Galois Theory. With A. Bachmayr and D. Harbater and F. Pop..
  J. Inst. Math. Jussieu 20 (2021), no. 6, 1931-1946.
  

• Free differential Galois groups. With A. Bachmayr , D. Harbater and M. Wibmer. Trans. Amer. Math. Soc. 374 (2021), no. 6, 4293-4308.
  

• Local-global principles for tori over arithmetic curves. With J.-L. Colliot-Thélène, D. Harbater, D. Krashen, R. Parimala and V. Suresh. Algebr. Geom. 7 (2020), no. 5, 607-633.

• Local-global Galois theory of arithmetic function fields. With D. Harbater, D. Krashen, R. Parimala and V. Suresh.
  Israel Journal of Mathematics, vol. 232, no. 2 (2019), 849-882.
  

• Local-global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields. With J.-L. Colliot-Thélène, D. Harbater, D. Krashen, R. Parimala and V. Suresh. Transactions of the AMS, vol. 372 (2019), no. 8, 5263-5286. DOI.
  

• Differential Embedding Problems over Laurent series fields. With A. Bachmayr and D. Harbater.
  Journal of Algebra, vol. 513 (2018), 99-112.

• Differential Embedding Problems over Complex Function Fields. With A. Bachmayr, D. Harbater and M. Wibmer.
  Documenta Mathematica, vol. 23 (2018), 241-291.

• Differential Galois groups over Laurent series fields.
  With A. Bachmayr and D. Harbater. Proceedings of the London Mathematical Society, vol. 112, no.3 (2016), 455-476.
  

• Local-Global Principles for Torsors over Arithmetic Curves. With D. Harbater and D. Krashen.
  American Journal of Mathematics, vol 137, no. 6 (2015), 1559-1612.
  

• Refinements to Patching and Applications to Field Invariants. With D. Harbater and D. Krashen.
  International Mathematics Research Notices, 2015; doi: 10.1093/imrn/rnu278. Published online January, 2015, at imrn.oxfordjournals.org.
  

• Local-global principles for Galois cohomology. With D. Harbater and D. Krashen.
  Commentarii Math. Helv., vol. 89, no. 1 (2014), 215-253.

• Weierstrass Preparation and Algebraic Invariants. With D. Harbater and D. Krashen.
  Math. Ann. 356, Issue 4 (2013), 1405--1424.
  

• Patching Subfields of Division Algebras. With D. Harbater and D. Krashen.
  Trans. Amer. Math. Soc. 363 (2011), no. 6, 3335--3349.
  

• Patching over Fields. With D. Harbater.
  Israel J. Math. 176 (2010), 61--107.
  

• Applications of Patching to Quadratic Forms and and Central Simple Algebras. With D. Harbater and D. Krashen.
  Invent. Math. 178 (2009), No.2, 231--263.
  

• A Local-Global Principle for Algebraic Group Actions and Applications to Quadratic Forms (joint with David Harbater, Daniel Krashen).
  In: Quadratic Forms and Linear Algebraic Groups, Oberwolfach reports 25/2009, European Mathematical Society.
  

• A Local-Global Principle for Homogeneous Spaces and Applications (joint with David Harbater, Daniel Krashen).
  In: Field Arithmetic, Oberwolfach reports 5/2009, European Mathematical Society.
  

• Jacobians of Reflection Groups. With Anne V. Shepler .
  Trans. Amer. Math. Soc. 360, No.1, 123-133 (2008).

• Patching and differential Galois groups (joint work with David Harbater).
  In: Arithmetic and Differential Galois Groups, Oberwolfach reports 4, No.2, European Mathematical Society (2007).

• Reflection Groups and Differential Forms. With Anne V. Shepler . Math. Res. Lett. 14, No. 5-6, 955-971 (2007).

• On the inverse problem in differential Galois theory.
  J. Reine Angew. Math. (Crelle) 586, 21--44 (2005).

• Invariants and Differential Galois Groups in Degree 4
  In: Differential Galois Theory, Banach Center Publications Vol. 58, T. Crespo and Zbigniew Hajto (eds.), 2002.

• Transvection Free Groups and Invariants of Polynomial Tensor Exterior Algebras
  Transformation Groups, Vol. 6, No. 2, 2001, pp. 157-164

Notes etc.

• Widening the pipeline. With Mona Merling. AMS Early Career Section. Notices of the AMS 67, No. 11, 1738-1740 (2020).

• Preparing your results for publication. AMS Early Career Section. Notices of the AMS 66, No. 3, 359-360 (2019).

• Thinking positive: Arithmetic Geometry in Characteristic p (with R. Bell, V. Karemaker, P. Srinivasan, and I. Vogt). Notices of the AMS 66, No. 2, 239-241 (2019).

• Division algebras and patching (with D. Harbater) . Lecture notes for the 2012 Arizona Winter School. 2012 manuscript.

• Symmetrien von Differentialgleichungen. In: Facettenreiche Mathematik, Katrin Wendland, Annette Werner (eds.), Vieweg+Teubner 2011.

• Neue Bücher aus Oberwolfach. Mit Sebastian Walcher. In: Mitteilungen der DMV 19-1 (2011).

• Berechnung der Galoisgruppe einer Differentialgleichung. In: Computeralgebra-Rundbrief 35 , 2004.

• Differential Galois Theory in Positive Characteristic
  Notes from a class given by B.H. Matzat, IWR-Preprint No. 2001-35

Dissertation

• On the Inverse Problem in Differential Galois Theory
  available from www.ub.uni-heidelberg.de/archiv/3085