3 problems

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The bounded PAC conjecture for infinite simple fields
A field is bounded if it has only finitely many extensions of each given finite degree, and it is PAC if every geometrically irreducible variety over it has a rational point. Bound…
Conjectureopenfield-arithmetic pseudo-algebraically-closed-fields simple-theoriesarXiv posted 2 days ago
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The PAC conjecture for the maximal solvable extension of the rationals
Let $\mathbb{Q}_{\mathrm{solv}}$ denote the maximal solvable extension of $\mathbb{Q}$ . PAC conjecture. The field $\mathbb{Q}_{\mathrm{solv}}$ is pseudo-algebraically closed (PAC).…
Conjectureopenfield-arithmetic pseudo-algebraically-closed-fieldsarXiv posted 2 days ago
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Ax's conjecture that perfect PAC fields are of type $C_{1}$
Ax's conjecture. Every perfect PAC field is of type $C_{1}$ .
Conjectureopenfield-arithmetic pseudo-algebraically-closed-fieldsarXiv posted 2 days ago

The bounded PAC conjecture for infinite simple fields