8 papers
The cohomological Kudla conjecture for unitary Shimura varieties
François Greer, Salim Tayou
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature and…
Modularity of special cycles on Shimura varieties: a survey
François Greer, Salim Tayou
We survey recent results on a conjecture of Kudla regarding the modularity of generating series of special cycle classes in toroidal compactifications of orthogonal and unitary Shi…
On the non-abelian Hodge locus I
Philip Engel, Salim Tayou
We partially resolve conjectures of Deligne and Simpson concerning -local systems on quasi-projective varieties that underlie a polarized variation of Hodge structure.…
Shafarevich's conjecture for families of hypersurfaces over function fields
Philip Engel, Alice Lin, Salim Tayou
Given a smooth quasi-projective complex algebraic variety , we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hyper…
The Zilber-Pink conjecture for varieties not defined over
Bruno Klingler, Salim Tayou
In this note, we prove the Zilber--Pink conjecture for subvarieties of mixed Shimura varieties, which are not defined over~ in a strong sense. We prove simila…
Mixed mock modularity of special divisors
Philip Engel, François Greer, Salim Tayou
We prove that the generating series of special divisors in toroidal compactifications of orthogonal Shimura varieties is a mixed mock modular form. More precisely, we find an expli…