Algebraic and Arithmetic Geometry Seminar

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

by Mattia Talpo (Università di Pisa)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


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.