ISITE-BFC Open research project « MYAV » (+picture)
Motivic invariants of algebraic varieties Frédéric DEGLISE, CNRS/IMB in collaboration with LMB
It is a major insight of the preceding two centuries that one can use a geometrical language to study the olutions of a given set of polynomial equations with coefficients in an arbitrary field, such as the omplex numbers or even in an arbitrary ring, such as the integers. The corresponding objects, called lgebraic varieties, are extremely rich and mysterious due to their dual nature, geometric and rithmetic. The driving force of the project is the use of the recent and powerful theory of motivic A1- omotopy introduced by Voevodsky to produce new, and study classical, invariants of algebraic arieties of both geometric and arithmetic nature. The expected applications have a very wide range: dvances in the understanding of Voevodsky’s theory, producing new knowledge in affine algebraic eometry, extending previously known computations of invariants for families of algebraic varieties, nd improvement of our arithmetical knowledge of certain kinds of algebraic varieties.