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David Roberts ♦
David Roberts ♦
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Classical Galois theory states that the etale topos X of a field k is equivalent to the classifying topos of the absolute Galois group of k.

(Marc Hoyois, Higher Galois theory, $\S$3, arXiv:https://arxiv.org/abs/1506.07155, doi:j.jpaa.2017.08.010)

I would like to know how is passing from Classical Galois theory (with classical I mean the Galois theory obtained with Grothendieck fundamental group, I know this is not very classic...) to the classical Galois theory referenced (an equivalence of topos, I know this doesn't looks classic also...)?

And, I Would like to know if this equivalence has been studied for schemes and not only for fields...

Classical Galois theory states that the etale topos X of a field k is equivalent to the classifying topos of the absolute Galois group of k.

https://arxiv.org/abs/1506.07155

I would like to know how is passing from Classical Galois theory (with classical I mean the Galois theory obtained with Grothendieck fundamental group, I know this is not very classic...) to the classical Galois theory referenced (an equivalence of topos, I know this doesn't looks classic also...)?

And, I Would like to know if this equivalence has been studied for schemes and not only for fields...

Classical Galois theory states that the etale topos X of a field k is equivalent to the classifying topos of the absolute Galois group of k.

(Marc Hoyois, Higher Galois theory, $\S$3, arXiv:1506.07155, doi:j.jpaa.2017.08.010)

I would like to know how is passing from Classical Galois theory (with classical I mean the Galois theory obtained with Grothendieck fundamental group, I know this is not very classic...) to the classical Galois theory referenced (an equivalence of topos, I know this doesn't looks classic also...)?

And, I Would like to know if this equivalence has been studied for schemes and not only for fields...

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Galoisianis
Galoisianis
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Galois theory, topos vs fundamental groups

Classical Galois theory states that the etale topos X of a field k is equivalent to the classifying topos of the absolute Galois group of k.

https://arxiv.org/abs/1506.07155

I would like to know how is passing from Classical Galois theory (with classical I mean the Galois theory obtained with Grothendieck fundamental group, I know this is not very classic...) to the classical Galois theory referenced (an equivalence of topos, I know this doesn't looks classic also...)?

And, I Would like to know if this equivalence has been studied for schemes and not only for fields...