Logarithmic Structures of Fontaine-Illusie. II ---Logarithmic Flat Topology

This is Part II of the author's paper Logarithmic structures of Fontaine-Illusie. We discuss log flat topology and log flat descent. We study the first log flat cohomology $H^1(X_{\log, \text{fl}}, G)$ for various sheaves of groups $G$, for example, $G=GL_n$, finite flat commutative group schemes, the log multiplicative group $M^{\text{gp}}$, etc.