Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic representations plus field a...

We give a group theoretic definition of “local models” as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are ob...

Comparative political economy is often based on the premise that the latter is true. In particular, the now classic Varieties of Capitalism (VofC) comparative approach postulates two types of institutional frameworks. The general idea was that each institutional solution generates positive externalities which may or may not be captured by specific solutions in other institutional domains. There...

In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism (satisfying certain conditions) from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme. The proof uses the theory of “regular log schemes ” – i.e., schemes with singularities like those of...

Theorem 1.1 (Chudnovsky’s theorems). Let Λ = Zω+Zω′ ⊂ C be a lattice with invariants g2, g3, Weierstrass functions ℘, ζ and quasi-periods η, η′, all defined in the usual way (see [Sil94]). Each of the sets below contains at least two algebraically independent numbers : first (1) {g2, g3, η ω , π ω}, (2) {g2, g3, ω, η, ω′, η′}; if we assume g2, g3 ∈ Q̄ : (3) { η ω , π ω}, (4) {ω, ω′, η, η′}; and ...

Motivated by the Strominger-Yau-Zaslow conjecture, we study fibre spaces whose total space has trivial canonical bundle. Especially, we are interest in CalabiYau varieties with fibre structures. In this paper, we only consider semi-stable families. We use Hodge theory and the generalized Donaldson-Simpson-Uhlenbeck-Yau correspondence to study the parabolic structure of higher direct images over...