In this paper we prove the following results: $1) $ We show that any arithmetic quotient of a
homogeneous space admits a natural real semi-algebraic structure for which its Hecke …

We give a proof of the André-Oort conjecture for A_g---the moduli space of principally
polarized abelian varieties. In particular, we show that a recently proven``averaged" version …

Abstract We extend the Ax–Schanuel theorem recently proven for Shimura varieties by Mok–
Pila–Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge …

Given a point ξ ξ on a complex abelian variety A, its abelian logarithm can be expressed as a
linear combination of the periods of A with real coefficients, the Betti coordinates of ξ ξ. When …

In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the-function
and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura …

Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …

Shimura varieties are algebraic varieties of enormous interest. Introduced by Shimura and
Deligne in order to generalize the modular curves, they play nowadays a central role in the …

We consider the Beilinson-Bloch heights and Abel-Jacobian periods of homologically trivial
Chow cycles in families. For the Beilinson-Bloch heights, we show that for any $ g\ge 3$, we …

The Ax–Schanuel conjecture for variations of mixed Hodge structures | Mathematische
Annalen Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

We present a conjecture on the geometry of the Hodge locus of a (graded polarizable,
admissible) variation of mixed Hodge structure over a complex smooth quasi-projective …