Faltings heights of abelian varieties with complex multiplication
F Andreatta, E Goren, B Howard… - Annals of …, 2018 - projecteuclid.org
Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic
space over Q of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the …
space over Q of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the …
The André-Oort conjecture for 𝒜_g
J Tsimerman - Annals of Mathematics, 2018 - projecteuclid.org
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 …
polarized abelian varieties. In particular, we show that a recently proven``averaged" version …
Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
Given a K3 surface X over a number field K with potentially good reduction everywhere, we
prove that the set of primes of K where the geometric Picard rank jumps is infinite. As a …
prove that the set of primes of K where the geometric Picard rank jumps is infinite. As a …
[HTML][HTML] CM values of higher automorphic Green functions for orthogonal groups
Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the
automorphic Green function G_s (z_1, z_2) G s (z 1, z 2) for the elliptic modular group at …
automorphic Green function G_s (z_1, z_2) G s (z 1, z 2) for the elliptic modular group at …
Arithmetic of Borcherds products
B Howard, KM Pera - arXiv preprint arXiv:1710.00347, 2017 - arxiv.org
arXiv:1710.00347v2 [math.NT] 21 Feb 2020 Page 1 arXiv:1710.00347v2 [math.NT] 21 Feb
2020 ARITHMETIC OF BORCHERDS PRODUCTS BENJAMIN HOWARD AND KEERTHI …
2020 ARITHMETIC OF BORCHERDS PRODUCTS BENJAMIN HOWARD AND KEERTHI …
Co-rank Arithmetic Siegel--Weil III: Geometric local-to-global
RC Chen - arXiv preprint arXiv:2405.01428, 2024 - arxiv.org
This is the third in a sequence of four papers, where we prove the arithmetic Siegel--Weil
formula in co-rank $1 $ for Kudla--Rapoport special cycles on exotic smooth integral models …
formula in co-rank $1 $ for Kudla--Rapoport special cycles on exotic smooth integral models …
On two arithmetic theta lifts
S Ehlen, S Sankaran - Compositio Mathematica, 2018 - cambridge.org
Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached
to special cycles on Shimura varieties of orthogonal and unitary type, which play a key role …
to special cycles on Shimura varieties of orthogonal and unitary type, which play a key role …
The large Galois orbits conjecture under multiplicative degeneration
C Daw, M Orr - arXiv preprint arXiv:2306.13463, 2023 - arxiv.org
We establish the PEL type large Galois orbits conjecture for Hodge generic curves in
$\mathcal {A} _g $ possessing multiplicative degeneration. Combined with our earlier works …
$\mathcal {A} _g $ possessing multiplicative degeneration. Combined with our earlier works …
Big Heegner points, generalized Heegner classes and -adic -functions in the quaternionic setting
M Longo, P Magrone, ER Walchek - arXiv preprint arXiv:2401.03439, 2024 - arxiv.org
The goal of this paper is to study the $ p $-adic variation of Heegner points and generalized
Heegner classes for ordinary families of quaternionic modular forms. We compare classical …
Heegner classes for ordinary families of quaternionic modular forms. We compare classical …
Reductions of abelian surfaces over global function fields
D Maulik, AN Shankar, Y Tang - Compositio Mathematica, 2022 - cambridge.org
Let $ A $ be a non-isotrivial ordinary abelian surface over a global function field of
characteristic $ p> 0$ with good reduction everywhere. Suppose that $ A $ does not have …
characteristic $ p> 0$ with good reduction everywhere. Suppose that $ A $ does not have …