Triangulated categories of log-motives over a field

Abstract 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 DM(k). The affine line is replaced in this context by the “cube” (P^1, \infty), i.e. the log scheme 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).