Geodesic
Differential Embedding Problems over Complex Function Fields
Documenta mathematica, Tome 23 (2018), pp. 241-291
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We introduce the notion of differential torsors, which allows the adaptation of constructions from algebraic geometry to differential Galois theory. Using these differential torsors, we set up a general framework for applying patching techniques in differential Galois theory over fields of characteristic zero. We show that patching holds over function fields over the complex numbers. As the main application, we prove the solvability of all differential embedding problems over complex function fields, thereby providing new insight on the structure of the absolute differential Galois group, i.e., the fundamental group of the underlying Tannakian category.
DOI : 10.4171/dm/618
Classification : 12H05, 14H55, 20G15, 34M50
Mots-clés : Riemann surfaces, embedding problems, differential algebra, linear algebraic groups and torsors, patching, Picard-Vessiot theory, inverse differential Galois problem 
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     author = {Annette Bachmayr and David Harbater and Michael Wibmer and Julia Hartmann},
     title = {Differential {Embedding} {Problems} over {Complex} {Function} {Fields}},
     journal = {Documenta mathematica},
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     year = {2018},
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     doi = {10.4171/dm/618},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/618/}
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Annette Bachmayr; David Harbater; Michael Wibmer; Julia Hartmann. Differential Embedding Problems over Complex Function Fields. Documenta mathematica, Tome 23 (2018), pp. 241-291. doi: 10.4171/dm/618

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