Alterations and Resolution of Singularities

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Abstract

On July 26, 1995, at the University of California, Santa Cruz, a young Dutch mathematician by the name Aise Johan de Jong made a revolution in the study of the arithmetic, geometry and cohomology theory of varieties in positive or mixed characteristic. The talk he delivered, first in a series of three entitled “Dominating Varieties by Smooth Varieties”, had a central theme: a systematic application of fibrations by nodal curves. Among the hundreds of awe-struck members of the audience, participants of the American Mathematical Society Summer Research Institute on Algebraic Geometry, many recognized the great potential of Johan de Jong’s ideas even for complex algebraic varieties, and indeed soon more results along these lines began to form.