Differential Embedding Problems over Laurent series fields

Annette Bachmayr; David Harbater; Julia Hartmann

Differential Embedding Problems over Laurent series fields

Commutative Algebra 2018-02-07 v2

Authors: Annette Bachmayr , David Harbater , Julia Hartmann

Abstract

We solve the inverse differential Galois problem over the fraction field of $k[[t,x]]$ and use this to solve split differential embedding problems over $k((t))(x)$ that are induced from $k(x)$ . The proofs use patching as well as prior results on inverse problems and embedding problems.

Keywords

galois theory

Cite

@article{arxiv.1710.02502,
  title  = {Differential Embedding Problems over Laurent series fields},
  author = {Annette Bachmayr and David Harbater and Julia Hartmann},
  journal= {arXiv preprint arXiv:1710.02502},
  year   = {2018}
}

Comments

13 pages; simplified Sections 1-3 (resulting in a renumbering of the statements in Section 1-2), added Proposition 1.4, added Remark 3.4, streamlined proof of Theorem 4.2, added Remark 4.4

Differential Embedding Problems over Laurent series fields

Abstract

Keywords

Cite

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