All Questions
Tagged with fundamental-group galois-theory
14 questions
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Topos-theoretic Galois theory
This page is an overview of some of the types of "Galois theories" there are. One of the most basic type is the fundamental theorem of covering spaces, which says, roughly, that for each ...
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Do surface groups embed into PSL_2 over a real quadratic integer ring?
$\DeclareMathOperator\PSL{PSL}$ Let $ \mathbb{Z} $ be the ring of integers and $ \mathbb{R} $ the field of real numbers. Let $ \Sigma_g $ be a surface of genus $ g \geq 2 $. Let $ \pi_1(\Sigma_g) $ be ...
- 4,081
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Is $\operatorname{Aut}(\mathcal{M})$ a fundamental group in Grothendieck's sense?
This question is a follow-up to Are there infinitely many L-rigs? and to Is an automorphic form of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ determined by its L-function?.
I copy paste a deepl ...
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Galois theory of ramified coverings vs classical Galois theory
That's an exact copy of my former MSE question I asked a couple of weeks ago and unfortunately not got the answer I was looking for.
The question adresses reuns' answer in this thread: Algebraic ...
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Relationships among constructions of fundamental group for schemes
There seem to be several constructions of fundamental group for schemes and stacks: by Grothendieck, Deligne, Nori, Noohi, Esnault-Hai, Vakil-Wickelgren, perhaps others as well. I am trying to ...
- 447
4
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Geometric fundamental group and algebraically closed residue field
my questions relates to the following talk of Tsuji:
https://www.youtube.com/watch?v=2brDj26phP0
At around 10:30 of the video, Tsuji is interrupted by a man stating that his construction does not ...
- 455
9
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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.
(Marc Hoyois, Higher Galois theory, $\S$3, arXiv:1506....
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8
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Inverse galois problem and étale homotopy
Is there any relation between étale homotopy theory (Grothendieck-Galois theory) and the inverse Galois problem?...I mean...in classical homotopy theory, every finite group $G$ realizes as a "Galois ...
user95283
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Profinite groups as étale fundamental groups
Does every profinite group arise as the étale fundamental group of a connected scheme?
Equivalently, does every Galois category arise as the category of finite étale covers of a connected scheme?
...
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19
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What are the different theories that the motivic fundamental group attempts to unify?
I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert.
In http://www.math.ias.edu/files/deligne/...
- 6,348
13
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What are Galois Categories used for?
Galois categories are introduced (for the first time?) in SGA1, but here's an English introduction that's available online: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Lynn.pdf
It ...
23
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Grothendieck's Galois Theory today
I have recently become aware of, and started to study in my free time (abundant in these summer months) Grothendieck's Galois Theory (GGT), as formulated in SGA 1 and later by Grothendieck's ...
- 1,539
32
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Fundamental groups of topoi
Just yesterday I heard of the notion of a fundamental group of a topos, so I looked it up on the nLab, where the following nice definition is given:
If $T$ is a Grothendieck topos arising as category ...
- 4,450
73
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10
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Galois groups vs. fundamental groups
In a recent blog post Terry Tao mentions in passing that:
"Class groups...are arithmetic analogues of the (abelianised) fundamental groups in topology, with Galois groups serving as the analogue ...
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