Algebraic and Arithmetic Geometry Seminar

# Triangulated categories of log-motives over a field

## by Federico Binda (Università di Milano Statale)

Europe/Rome
Aula Magna (Dipartimento di Matematica)

### Aula Magna

#### Dipartimento di Matematica

Description

In this talk, I will give an overview of the construction of a triangulated category of motives for log smooth log schemes over a field $k$, based on the notion of finite log correspondence, in analogy to Voevodsky’s $\mathsf{DM}(k)$. The affine line is replaced in this context by the “cube” $(\mathbb{P}^1, \infty)$, i.e. the log scheme $\mathbb{P}^1_1$ with log structure coming from the divisor at infinity, as one does in the theory of motives with modulus à la Kahn-Saito-Yamazaki. This is a joint work in progress with Doosung Park (Zurich) and Paul Arne Ostvaer (Oslo).