Connections and Related Integral Structures on the Universal Extension of an Elliptic Curve

§0. Introduction §1. The Étale Integral Structure on the Universal Extension §2. The Étale Integral Structure for an Ordinary Elliptic Curve §2.1. Some p-adic Function Theory §2.2. The Verschiebung Morphism §3. Compactified Hodge Torsors §4. The Étale Integral Structure on the Hodge Torsors §4.1. Notation and Set-Up §4.2. Degenerating Elliptic Curves §4.3. Ordinary Elliptic Curves §4.4. The General Case §5. Construction of the Connection §5.1. Complex Analogue §5.2. The Schematic Case §6. The Schottky-Theoretic Hodge-Arakelov Comparison Isomorphism §7. Crystalline Theta Expansions §7.1. Generalities on Higher p-Curvatures §7.2. Application to Theta Expansions §8. “Griffiths Semi-Transversality” §8.1. The Kodaira-Spencer Morphism of the Crystalline Theta Object §8.2. Calculation of the Higher p-Curvatures §8.3. Hasse-type Invariants of the Crystalline Theta Object §9. Relation to the Theory of [Mzk1]