|
so:text
|
Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category which in some intuitive sense “softens algebraic geometry” so as to allow for a good notion of homotopy in an algebro-geometric setup and is sufficiently directly connected to concrete algebraic geometry to have already yielded some extraordinary applications. The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so throughout the current century. (en) |
