Patching over fields
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- Harbater, D. & Hartmann, J. Isr. J. Math. (2010) 176: 61. doi:10.1007/s11856-010-0021-1
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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.