The Role of Valuation Theory in Resolution of Singularities
by
Shreeram S. Abhyankar
Purdue

The use of valuation theory in resolution of singularities was pioneered by Zariski during 1939-1944. As Zariski's pupil, I inherited this fondness for valuation theory. In my Ph.D. thesis of 1955, I heavily used valuation theory to prove resolution of singularities of algebraic surfaces over ground fields of nonzero characteristic. Later on, in 1963 and 1966, I extended the use of valuation theory to prove resolution of singularities of arithmetic surfaces and resolution of singularities of three-dimensional algebraic varieties over ground fields of nonzero characteristic. In this talk I shall explain this use of valuation theory. It is a challange to the younger generation to extend resolution of singularities to still higher dimensions.

Date received: March 31, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-19.