Doosung Park (Berkeley) Triangulated categories of motives over fs log schemes

Triangulated categories of motives over schemes are sort of the "universal derived categories" among various derived categories obtained by various cohomology theories like l-adic cohomology. Ayoub constructed them using the A1-homotopy equivalences and étale topology. I will introduce the construction of triangulated categories of motives over fs log schemes. Fs log schemes are kinds of "schemes with toroidal boundary," and A1-homotopy equivalences and étale topology are not enough to obtain all homotopy equivalences between fs log schemes. I will explain what extra homotopy equivalences and topologies are neeeded.