Diophantine and cohomological dimensions
classification
🧮 math.RA
keywords
dimensiondiophantinecohomologicalfieldboundsdimensionsequalexplicit
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We give explicit linear bounds on the p-cohomological dimension of a field in terms of its Diophantine dimension. In particular, we show that for a field of Diophantine dimension at most 4, the 3-cohomological dimension is less than or equal to the Diophantine dimension.
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