2017/08/31 by Brouette, Quentin, Cousins, Greg, Pillay, Anand +1
#03C10 #03C45 #12H05 #34M50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1709.00046
We prove that if T is a theory of large, bounded, fields of characteristic zero, with almost quantifier elimination, and TD is the model companion of T + "D is a derivation", then for any model U of TD, and differential subfield K of U whose field of constants is a model of T, and linear differential equation DY = AY over K, there is a Picard-Vessiot extension L of K for the equation which is embedded in U over K Likewise for logarithmic differential equations over K on connected algebraic groups over the constants of K and the corresponding strongly normal extensions of K.