## CANCELLED

#### Paola D'Aquino (Campania )

We give a description of the spectra of $$\hat{\mathbb{Z}}$$ and of the finite adeles using ultraproducts. In describing the prime ideals and the localizations of $$\hat{\mathbb{Z}}$$ , ultrapowers of the group $$\mathbb{Z}$$ and ultraproducts of the rings of p-adic integers are used (joint work with A. Macintyre and M. Otero.)