Picard rank jumps for K3 surfaces with bad reduction

(K3) surfaces and Enriques surfaces (14J28) Arithmetic aspects of modular and Shimura varieties (11G18) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Cites Work

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The Tate conjecture for \(K3\) surfaces in odd characteristic
Equidistribution of special subvarieties
Representations of integers by an invariant polynomial and unipotent flows
Hypersymmetric Abelian varieties
Hyperbolic distribution problems and half-integral weight Maass forms
Borcherds products on \(O(2,l)\) and Chern classes of Heegner divisors
Faltings heights of abelian varieties with complex multiplication
Exceptional isogenies between reductions of pairs of elliptic curves
Singular symmetric matrices
Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli
The Gross-Kohnen-Zagier theorem in higher dimensions
Picard ranks of \(K3\) surfaces over function fields and the Hecke orbit conjecture
Special cycles on toroidal compactifications of orthogonal Shimura varieties
Exceptional splitting of reductions of abelian surfaces
On the equidistribution of some Hodge loci
The structure of integral parabolic subgroups of orthogonal groups
On the Picard number of \(K3\) surfaces over number fields
Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
Holomorphic projections and Ramanujan’s mock theta functions
Integral models for Shimura varieties of abelian type
Local families of K3 surfaces and applications
Boundary cohomology of Shimura varieties, III: - Coherent cohomology on higher-rank boundary strata and applications to Hodge theory
Arithmetic divisors on orthogonal and unitary Shimura varieties
Toroidal compactifications of integral models of Shimura varieties of Hodge type
Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
Equidistribution of Hodge loci II
Reductions of abelian surfaces over global function fields
Integral canonical models for Spin Shimura varieties
Height pairings on orthogonal Shimura varieties
On the distribution of the Hodge locus
On the ordinary Hecke orbit conjecture

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