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The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along… (More)
1 Statement of the result Consider the second order linear differential equation fl=ry, withrc Q(z). Let Qc~ denote the algebraic closure of the field of rational numbers Q and let G denote thedifferential Galois group over Qcl(z) of this equation. Then G C S/(2, Qct). F~r any solution y # O of the equation the element u = $ satisfies the Riccati equation… (More)
a r t i c l e i n f o a b s t r a c t The notion of strict equivalence for order one differential equations of the form f (y , y, z) = 0 with coefficients in a finite extension K of C(z) is introduced. The equation gives rise to a curve X over K and a derivation D on its function field K (X). Procedures are described for testing strict equivalence, strict… (More)
We survey some constructive aspects of dierential Galois theory and indicate some analogies between ordinary Galois theory and dier-ential Galois theory in characteristic zero and nonzero.