Families of Abelian Varieties

By David Mumford. 2004

64 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2bdee907c3db1126466cd00a63b6139e14dae1e0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. E. Viehweg
2. Martin Moeller
3. J. S. Milne
4. Jan Rohde
5. K. Zuo

Citations in the corpus

• Equidistribution in Families of Abelian Varieties and Uniformity (2021, unknown): “This follows, for example, by combining [68, Lemma 2.1.9], [ 61, Corollary of Theorem 1] and [63, Proposition 1].”
• Variations of Hodge structures of a Teichmüller curve (2006, background): “Mumford defines a Shimura variety (see [Mu66], [Mu69]) as the coarse moduli space M (Hg) for the functor M (Hg) representing isomorphism classes of polarized abelian varieties with special Mumford-Tate group equal to a subgroup of Hg.”
• Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (2007, methodology): “Tate have originally constructed families of abelian varieties over Hermitian symmetric domains by using the Hodge group instead of the Mumford-Tate group (see [46] and [47]) as we will do in a similar way.”
• Shimura Varieties and Moduli (2011, background): “2 In particular, we have shown that the curve SN , constructed by Mumford purely in terms of algebraic geometry, is isomorphic by the obvious map to the curve YN , constructed analytically.”
• A CHARACTERIZATION OF CERTAIN SHIMURA CURVES IN THE MODULI STACK OF ABELIAN VARIETIES (2002, background): “As we will see in Section 4 Theorem 0.2 follows from the existence of too many endomorphisms of the general fibre of f : X → Y , which in turn implies the existence of too many cycles on the general fibre of X ×Y X.”
• COMPLEX MULTIPLICATION, GRIFFITHS-YUKAWA COUPLINGS, AND RIGIDITY FOR FAMILIES OF HYPERSURFACES (2003, methodology): “Quintic threefolds with complex multiplication Recall the definition of the special Mumford-Tate group (called Hodge group in [17] and [18]), Let V be a Q-vector space with a Hodge structure of weight k.”