The problem of comparing algebraic and complex analytic geometry is a very classical question. In the case of proper algebraic varieties, the question has been settled by Serre's famous GAGA theorem. In the non-proper case, this theorem does not hold but some comparison results between analytic and algebraic objects have been obtained when the properness assumption is replaced by a growth condition on the analytic functions considered. In this talk, we will present an approach based on the theory of tempered holomorphic functions which allows to obtain a partial GAGA type theorem for non-proper smooth algebraic varieties.

### Math-Physics Joint Seminar

Thursday, February 16, 2017 - 4:30pm

#### Francois Petit

University of Luxembourg