Introduction Notations Moduli spaces of abelian varieties with real multiplication Properties of $\mathcal{G}$ Hilbert modular forms The $q$-expansion map The partial Hasse invariants Reduceness of the partial Hasse invariants A compactification of $\mathfrak{M} (k, \mu_{pN})^{\…
Introduction Local cohomology groups Global cohomology groups and Selmer structures Kolyvagin systems Kolyvagin systems over principal artinian rings Kolyvagin systems over integral domains Examples Appendix A. Proof of Theorem 3.2.4 Appendix B. Proof of Theorem 4.3.3, by Benjam…
"The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell con…
"This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families, and on the canonical and subcanonical extensions of automorphic bundles. The results in this book serve as the logic…