On the History of Valuation Theory
by
Peter Roquette
Mathematisches Institut, Univ. Heidelberg

The first axiomatic definition of a valuation seems to have been stated by Josef Kürschák in a paper which appeared in Crelle's Journal in 1913. In the first part of my talk I shall try to exhibit the background and motivation of this paper, as well as the ensuing development and application of valuation theory within the framework of theory of algebraic numbers, including class field theory, in particular through the influence of Helmut Hasse.

While this concerns mainly valuations of rank 1, the second part of my talk will be devoted to the notion of general valuation as introduced by Wolfgang Krull in his seminal paper of 1932, also published in Crelle's Journal. Here, the application of valuation theory in the framework of algebraic geometry, as promoted by Oscar Zariski, will be the guideline of our investigation.

Finally, the role of valuations in model theory will be discussed (if time permits).

The talk (and its written version which will be available later) is meant as a first step towards a general and comprehensive treatment of the history of valuation theory.

Date received: July 5, 1999