We propose a conjecture combining the Mordell-Lang conjecture with an important special case of the André-Oort conjecture, and explain how existing results imply evidence for it. Mathematics Subject Classification: 14G35, 14K12 (11F32, 11F72, 11G15, 11G18)

This expository article introduces some conjectures and theorems related to the Faltings heights of abelian varieties with complex multiplication. The topics include the Colmez conjecture, the averaged Colmez conjecture, and the André–Oort conjecture.

Every homology or cohomology theory on a category ofE∞ ring spectra is Topological André–Quillen homology or cohomology with appropriate coefficients. Analogous results hold more generally for categories of algebras over operads. Mathematics Subject Classification (2000): 55P43, 55P48, 55U35

We explain how the approach of André and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.

No regular hyperoval of the Desarguesian affine plane AG(2, 2), with h > 1, is inherited by a dual André plane of order 2 and dimension 2 over its kernel.