1 Introduction
1.1 Notation and Conventions
2 Log Adic Spaces
2.1 Recollection on Monoids
2.2 Log Adic Spaces
2.3 Charts and Fiber Products
3 Log Smoothness and Log Differentials
3.1 Log Smooth Morphisms
3.2 Log Differentials
3.3 Sheaves of Log Differentials
4 Kummer étale Topology
4.1 The Kummer étale Site
4.2 Abhyankar's Lemma
4.3 Coherent Sheaves
4.4 Descent of Kummer étale Covers
4.5 Localization and Base Change Functors
4.6 Purity of Torsion Local Systems
5 Pro-Kummer étale Topology
5.1 The Pro-Kummer étale Site

Full Level Structures on Elliptic Curves
1 Overview
2 Level Structures on Elliptic Curves
3 The Ordinary Locus
4 Kunz's Theorem in Mixed Characteristic
References
The Saturated de Rham-Witt Complex for Schemes with Toroidal Singularities
Introduction
1 Dieudonné Complexes and Dieudonné Algebras
2 Dieudonné Complexes of Monoid Algebras
3 Idealized Monoid Algebras
4 Ideally Toroidal Schemes
5 Crystalline Cohomology
6 Log Schemes
7 The Hodge and Nygaard Filtrations
A Technicalities of Toric Differentials
References