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.