Development of Galois theory between arithmetics and topology (1850 to 1960)
A detailed survey on the development of Galois's theory is given, which covers the long time period between 1850 and 1960. There are results in function theory, algebraic topology and generalizations of separability connected with the Galois theory considered. Contributions of Puiseux, Hermite, Riemann, Jordan, Klein, Dyck, Dedekind, Weber and Zariski (related to function theory), Kronecker, A. Kneser, Steinitz, Krull, Noether, Artin (algebra) are discussed. Then an analogy between topology and Galois theory is given by use of Poincaré's fundamental group. It follows the existence theorem of Riemann-Enriques-Grauert-Remmert and a characterization of separability by means of differentials. The paper deals with the Galois theory of commutative rings (Auslander) and the schemes of Grothendieck, too. One can find a lot of names of mathematicians with data of birth and death and a useful rich bibliography.
scientific article; zbMATH DE number 1047104