Existential rank and essential dimension of diophantine sets

2021/02/13 by Daans, Nicolas, Dittmann, Philip, Fehm, Arno · 3 citations
#11U05 #11U09 #12L05 #12L12 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.06941

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.

Cited by

• Existentially defining valuations in function fields over large fields
• Decidability of polynomial equations over function fields in positive characteristic
• Serre's question on thin sets in projective space

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