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 …
On the averaged Colmez conjecture
X Yuan, SW Zhang - Annals of Mathematics, 2018 - JSTOR
The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with
complex multiplication in terms of some linear combination of logarithmic derivatives of Artin …
complex multiplication in terms of some linear combination of logarithmic derivatives of Artin …
On the arithmetic Siegel–Weil formula for GSpin Shimura varieties
C Li, W Zhang - Inventiones mathematicae, 2022 - Springer
We formulate and prove a local arithmetic Siegel–Weil formula for GSpin Rapoport–Zink
spaces, which is a precise identity between the arithmetic intersection numbers of special …
spaces, which is a precise identity between the arithmetic intersection numbers of special …
Applications of the hyperbolic Ax–Schanuel conjecture
C Daw, J Ren - Compositio Mathematica, 2018 - cambridge.org
In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the-function
and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura …
and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura …
[PDF][PDF] Efficient algorithms for abelian varieties and their moduli spaces
D Robert - 2021 - hal.science
Efficient algorithms for abelian varieties and their moduli spaces Page 1 HAL Id: tel-03498268
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …
[图书][B] Point-Counting and the Zilber–Pink Conjecture
J Pila - 2022 - books.google.com
Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
Modularity of generating series of divisors on unitary Shimura varieties
J Bruinier, B Howard, SS Kudla, M Rapoport… - arXiv preprint arXiv …, 2017 - arxiv.org
We form generating series of special divisors, valued in the Chow group and in the
arithmetic Chow group, on the compactified integral model of a Shimura variety associated …
arithmetic Chow group, on the compactified integral model of a Shimura variety associated …
Bi-algebraic geometry and the André-Oort conjecture
B Klingler, E Ullmo, A Yafaev - Algebraic geometry: Salt Lake …, 2018 - books.google.com
Shimura varieties are algebraic varieties of enormous interest. Introduced by Shimura and
Deligne in order to generalize the modular curves, they play nowadays a central role in the …
Deligne in order to generalize the modular curves, they play nowadays a central role in the …
Finiteness theorems for K3 surfaces and abelian varieties of CM type
M Orr, AN Skorobogatov - Compositio Mathematica, 2018 - cambridge.org
We study abelian varieties and K3 surfaces with complex multiplication defined over number
fields of fixed degree. We show that these varieties fall into finitely many isomorphism …
fields of fixed degree. We show that these varieties fall into finitely many isomorphism …