13 citations · 15 across the 9 of their papers we have counts for
13 papers
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…
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…
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…
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…
On the torsion locus of the Ceresa normal function
Matt Kerr, Salim Tayou
We prove that the positive-dimensional part of the torsion locus of the Ceresa normal function in is not Zariski dense when . Moreover, it has only finitel…
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.…
Vanishing of Brauer classes on K3 surfaces under reduction
Davesh Maulik, Salim Tayou
Given a Brauer class on a K3 surface defined over a number field, we prove that there exists infinitely many reductions where the Brauer class vanishes, under certain technical hyp…
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…
Picard rank jumps for K3 surfaces with bad reduction
Salim Tayou
Let be a K3 surface over a number field. We prove that has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar--Shan…
Equidistribution of Hodge loci II
Salim Tayou, Nicolas Tholozan
Let be a polarized variation of Hodge structure over a smooth complex quasi-projective variety . In this paper, we give a complete description of the typical Hodge l…
Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
Ananth N. Shankar, Arul Shankar, Yunqing Tang +1
Given a K3 surface over a number field with potentially good reduction everywhere, we prove that the set of primes of where the geometric Picard rank jumps is infinite.…
Rational curves on elliptic K3 surfaces
Salim Tayou
We prove that any non-isotrivial elliptic K3 surface over an algebraically closed field of arbitrary characteristic contains infinitely many rational curves. In the case when $…
On the equidistribution of some Hodge loci
Salim Tayou
We prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight with over complex, quasi-projective c…