"vast generalization" is a correct and usable phrase in written English.
It is typically used to refer to a broad or sweeping statement that is not based on specific evidence or data. Example: The politician's speech was filled with vast generalizations about the current state of the economy, without providing any concrete examples or statistics to support his claims.
The commutative case (which is essential even for the general pseudo-reductive case) is a corollary of a vast generalization of the Poitou-Tate nine-term exact sequence, from finite group schemes to arbitrary affine commutative group schemes of finite type.
This self-duality property admits a vast generalization leading to the notion of a Calabi-Yau algebra and, more generally, Calabi-Yau category.
It's a vast generalization, but we're writing briefly, so it has to suffice.
It's a vast generalization, but there's not a black person in America that doesn't know what a fist bump is.
It is difficult to make a vast generalization about the impact of flexibility because of the broad scope of biomechanical stresses and physical requirements throughout various athletic endeavors.
Our method may be viewed as a vast generalization of the Cohn Umans method, allowing for arbitrary bilinear operations in place of matrix-matrix product, and arbitrary algebras (particularly coordinate rings of schemes, cohomology rings of manifolds, PI algebras) in place of group algebras.
Athletes should likewise be shielded from such vast generalizations.
When he talks history, he spews vast generalizations like so many beads at Mardi Gras.
In my opinion, both criticisms reflect vast generalizations.
But to say that men in general aren't "man enough" is a vast, sweeping generalization.
Abstract: We will discuss the conjecture of Birch and Swinnerton-Dyer, which predicts deep connections between the L-function of an elliptic curve and its arithmetic, and the vast conjectural generalizations for motives due to Beilinson, Bloch and Kato.
