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Apr
12
asked Image of map of étale fundamental groups
Feb
22
awarded  Nice Answer
Feb
16
awarded  Favorite Question
Feb
11
asked Monomorphism in the category of schemes
Feb
10
comment Residue fields of schemes of finite type (over $\mathbb{Z}$)
@AriyanJavanpeykar, sure, but my point is that if $k(x) \rightarrow K$ is a strictly bigger field, than $x$ is a $K$-rational point whose residue field is not $K$. So your stated equality of sets between the set of closed points with residue field $\mathbb{F}_q$ and the set $X(\mathbb{F}_q)$ of $\mathbb{F}_q$-rational point need not hold in general. For example if $q = p^2$ and $X$ contains a point $x$ with residue field $\mathbb{F}_p$, than this point is not in the first set but it occurs in fact twice in the second set. Am I right?
Feb
9
comment Residue fields of schemes of finite type (over $\mathbb{Z}$)
Hi @AriyanJavanpeykar, great answer, thanks! Just one question: you say "the set of (closed) points with residue field $\mathbb{F}_q$ is the set $X(\mathbb{F}_q)$ of $\mathbb{F}_q$-rational points of $X$". But isn't this only true if $q$ is itself a prime number? If not, if $q = p^n$ with $n > 1$, then a point with residue field $\mathbb{F}_p$ will be in $X(\mathbb{F}_q)$, right?
Jan
12
awarded  Good Question
Jan
10
awarded  Nice Question
Nov
8
awarded  Nice Answer
Oct
30
awarded  Popular Question
Oct
27
comment An example of a map that is not unramified in a specific way
It is basically your example Georges but then with $\mathbb{Z}_p$ replaced by $k$. Thanks in any case for your great answer!
Oct
27
comment An example of a map that is not unramified in a specific way
Hi Georges and @AlexYoucis , how about the map $k \rightarrow k[x]$, the generic point of $\mathbb{A}^1$ is mapped to the unique point of $\operatorname{Spec}(k)$, resulting in $k = k_{(0)} \rightarrow k[x]_{(0)} = k(x)$ where 1. is satisfied but 2. not since the extension is infinite?
Oct
27
accepted An example of a map that is not unramified in a specific way
Oct
20
comment An example of a map that is not unramified in a specific way
Thanks! But this extension is still finite right? I was actually looking for an infinite extension (not necessarily inseparable).
Oct
20
comment An example of a map that is not unramified in a specific way
@AlexYoucis Woops I messed up the definition of finite type maps. ^^ But that makes me think, since the map $\kappa(x) \rightarrow \kappa(y) $ is of finite type doesn't that already imply it is finite? Or am I being silly again?
Oct
20
comment An example of a map that is not unramified in a specific way
Hi @AlexYoucis ! Thanks for your comments. But I just realised something, how about the map induced by $\mathbb{C} \rightarrow \mathbb{C}(T)$? Isn't it an example? Its fibers are obviously finite, which is quasi-finiteness of the map by definition right? So why does your logic not apply in this case?
Oct
20
asked An example of a map that is not unramified in a specific way
Jul
19
comment How to replace addition with multiplication to find the next integer value?
Hi Vita. First of all let me congratulate you with your mathematical curiosity! Keep asking yourself questions like these, and never worry about whether or not they are stupid questions!
Jul
18
awarded  Yearling
Jun
30
comment What are the most prominent uses of transfinite induction outside of set theory?
@CiaPan could you point me to a reference for that statement? Sounds intriguing..