Existential rank and essential dimension of diophantine sets

Abstract

We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points associated to such a definition.

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References in corpus (2)

• Multivariable polynomial injections on rational numbers
• A topological approach to undefinability in algebraic extensions of $\mathbb{Q}$

Cited by in corpus (1)

• $\mathbb{Q}\setminus \mathbb{Z}$ is diophantine over $\mathbb{Q}$ with 32 unknowns