Assuming the Bloch-Beilinson conjecture, the Chow group valued generating series for special cycles on orthogonal Shimura varieties over totally real fields is modular in all codimensions and for all d_+.
Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.
fields
math.NT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Remarks on generating series for special cycles
Assuming the Bloch-Beilinson conjecture, the Chow group valued generating series for special cycles on orthogonal Shimura varieties over totally real fields is modular in all codimensions and for all d_+.