G-functions of order two exist that are not polynomial expressions in algebraic pullbacks of hypergeometric functions, answering Siegel's problem negatively and adding counterexamples to Dwork's conjecture.
Generalised Andr\'e-Pink-Zannier Conjecture for Shimura varieties of abelian type
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we prove the generalised Andr\'e-Pink-Zannier conjecture (an important case of the Zilber-Pink conjecture) for all Shimura varieties of abelian type. Questions of this type were first asked by Y. Andr\'e in 1989. We actually prove a general statement for all Shimura varieties, subject to certain assumptions that are satisfied for Shimura varieties of abelian type and are expected to hold in general. We also prove another result, a p-adic Kempf-Ness theorem, on the relation between good reduction of homogeneous spaces over p-adic integers with Mumford stability property in p-adic geometric invariant theory.
fields
math.NT 1years
2025 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
On Siegel's problem and Dwork's conjecture for $G$-functions
G-functions of order two exist that are not polynomial expressions in algebraic pullbacks of hypergeometric functions, answering Siegel's problem negatively and adding counterexamples to Dwork's conjecture.