Subvarieties of Shimura varieties
By Bas Edixhoven, A. Yafaev. 2001
124 citations recorded by the source corpus.
7 Proof of the main result. 19 7.3 The case where is bounded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 7.4 The case where is not bounded. . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Both authors were partially supported by the European Research Training Network Contract HPRN-CT-200000120 “arithmetic algebraic geometry”. Adresses: IRMAR, Campus de Beaulieu, 35042 Rennes cedex, France; edix@maths.univ-rennes1.fr, ayafaev@maths.univ-rennes1.fr
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/05f09c78f43d2257b0fdddfb49909527005862b5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture (2012, background): “This statement is a variant of Proposition 4.3.9 of [7].”
- Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “As in [11], Proposition 2.2, a subvariety Z of Sh K ( G, X ) is a (weakly) special subvariety of Sh K ( G, X ) if and only if any irreducible component of the inverse image of Z in Sh K ad ( G ad , X ad ) is a (weakly) special subvariety of Sh K ad ( G ad , X ad ).”
- Period Mappings and Period Domains (2017, background): “Such a category does not exist yet, but several attempts have been made, the most successful one up to now being the Voevodsky triangulated category of motives (see Voevodsky et al., 2000; Levine, 1998, and Mazza et al., 2006). For a completely different approach, suggested by Nori, see Huber and Mü”
- Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points (2013, methodology): “The original André-Oort conjecture, in which one replaces “mixed Shimura variety” by “pure Shimura variety”, has been established in many cases (unconditionally or under GRH without using o-minimality) by Moonen [40], André [2], Edixhoven [24, 25], Edixhoven-Yafaev [27] and Yafaev [68, 69].”
- The André-Oort conjecture (2012, methodology): “In the characterization of [18], in order to obtain the irreducibility of TmZ the prime l must be outside some finite set PZ of primes.”
- Equidistribution of CM-points on quaternion Shimura varieties (2005, background): “The maximality condition of the Hodge-Tate group automatically holds in dimen- sion-one case (Proposition 7.2), and can be classified in dimension-2 case (Proposition 7.3).”
- Middle convolution of Fuchsian systems and the construction of rigid differential systems (2007, background): “Such differential systems are widely studied and are important in many branches of mathematics and physics, see [1], [7], [9], [10], [14], [16], and the references therein.”
- The Torelli locus and special subvarieties (2011, background): “The homomorphism h0 : S → CSp2g,R factors through MR. Conversely, if h ∈ Hg factors through MR then D acts by endomorphisms on the corresponding abelian variety.”
- O-minimality and the André-Oort conjecture for $\mathbb{C}^{n}$ (2011, result): “…by Zannier and implemented in three recent papers: a new proof of the Manin-Mumford conjecture by Pila-Zannier; a proof of a special (but new) case of Pink’s relative Manin-Mumford conjecture by Masser-Zannier; and new proofs of certain known results of André-OortManin-Mumford type by Pila.”
- A Combination of the Conjectures of Mordell-Lang and André-Oort (2005, background): “Thus it preserves the generalized Hecke orbit in the sense of 3.5, and the proposition follows.”
- CM points and quaternion algebras (2005, background): “3 of [6] and a variant of Proposition 2.”
- Special points on products of modular curves (2003, unknown): “Let n ≥ 3 be integer.”