Appears in collection : Conference on Arithmetic Geometry in honor of Luc Illusie

Many p-adic cohomology theories (e.g., de Rham, crystalline, prismatic) are known to have logarithmic analogs. I will explain how the theory of the “infinite root stack” (introduced by Talpo-Vistoli) gives an alternate approach to building the logarithmic theory (from the non-logarithmic one). As a consequence, one obtains an integral version of (log-)syntomic cohomology with comparisons to p-adic nearby cycles. Joint with Bhargav Bhatt and Dustin Clausen.