Algebraic and Arithmetic Geometry Seminar

# Topological realization over $\mathbb{C}((t))$ via Kato-Nakayama spaces

## by Mattia Talpo (Università di Pisa)

Europe/Rome
Aula Magna (Dipartimento di Matematica)

### Aula Magna

#### Dipartimento di Matematica

Description

I will report on some joint work with Piotr Achinger, about a “Betti realization” functor for varieties over the formal punctured disk $\mathsf{Spec}\mathbb{C}((t))$, i.e. defined by polynomials with coefficients in the field of formal Laurent series in one variable over the complex numbers. We give two constructions producing the same result, and one of them is via “good models” over the power series ring $\mathbb{C}[[t]]$ and the “Kato-Nakayama” construction in logarithmic geometry, that I will review during the talk.