Israel Journal of Mathematics

, Volume 176, Issue 1, pp 61–107

Patching over fields


DOI: 10.1007/s11856-010-0021-1

Cite this article as:
Harbater, D. & Hartmann, J. Isr. J. Math. (2010) 176: 61. doi:10.1007/s11856-010-0021-1


We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and vector spaces, rather than rings and modules. After presenting a self-contained development of this form of patching, we obtain applications to other structures such as Brauer groups and differential modules.

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Lehrstuhl A für MathematikRWTH Aachen UniversityAachenGermany