2d

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Rationally connected spaces over nonalgebraicallyclosed fields
@AntoineDucros If $X$ is a conic, then the second projection $p_2$ gives $X\times X$ the structure of a SeveriBrauer scheme over $X$, and since it has a section (the diagonal), it is isomorphic to $\mathbf P^1\times X$. 
Apr
22 
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Reduced scheme and closed points
@AdamTopaz Could you please precise what this "standard trick" is exactly? Thanks! 
Apr
22 
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NonArchimedean nonstandard models for R
Is it so different from the other answer? If you add a constant $t$ to the language with the axioms that it be greater than any integer $x$, then $t$ is transcendental and any model contains $F(t)$ — the simplifying point being that $F(t)$ is already real closed. 
Apr
21 
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Reduced scheme and closed points
@brunoh Note that Antoine Ducros has been careful enough to fill both the missing hypothesis in the statemetn and the details in the proof. :) 
Apr
21 
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Examples of common false beliefs in mathematics
This one I heard from a reputed colleague in another field, but I presume he didn't really think of it and only got influenced by the notation. 
Apr
21 
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Examples of common false beliefs in mathematics
@Michael Wasn't it the sum of the empty set of halfroots that was equal to $1/6$? This is at least what Demazure writes after writing Kac's character formula for the group $U(1)$. But his witty addition that “this would have unexpected consequences, especially regarding the teaching of mathematics in kindergarten” should not be have been taken seriously! 
Apr
21 
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Examples of common false beliefs in mathematics
@AkivaWeinberger: Yes, it is wrong. The closed unit ball of an normed vector space is compact if and only if the space is finite dimensional. 
Apr
21 
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What is the precise relationship between ominimal theory and Grothendieck's “Esquisse d'un programme”?
@EmilJeřábek Thanks for the correction. I edited accordingly. 
Apr
21 
awarded  Enlightened 
Apr
21 
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Examples of common false beliefs in mathematics
I meant that $VU$ cannot be a subspace since it doesn't contain 0. On the other hand, in any commutative ring where $1+1=0$, then the formula $(x+ y )^2=x^2+y^2$ holds. 
Apr
21 
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Examples of common false beliefs in mathematics
By the way, this fact is the basis for a beautiful proof of Hilbert's Nullstellensatz. 
Apr
21 
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Examples of common false beliefs in mathematics
@ThomasRot But it always fails, while $(x+y)^2=x^2+y^2$ sometimes holds, especially in characteristic 2. 
Apr
21 
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Examples of common false beliefs in mathematics
Exact. Moreover, if it were connected, its suspension $\mathbb S^1$ would be simply connected. 
Apr
21 
awarded  Nice Answer 
Apr
20 
awarded  Necromancer 
Apr
20 
revised 
What is the precise relationship between ominimal theory and Grothendieck's “Esquisse d'un programme”?
edit: corrections of 2 mistakes indicated in comments 
Apr
20 
comment 
What is the precise relationship between ominimal theory and Grothendieck's “Esquisse d'un programme”?
It is not clear to me that this requirement in Grothendieck's esquisse (“passing from $X$ to $\mathop{\rm Aut}(X)$ leaves the world of finite dimensional spaces”, he says) is satisfied by ominimal geometry. At least not obviously. 
Apr
20 
revised 
What is the precise relationship between ominimal theory and Grothendieck's “Esquisse d'un programme”?
add: complex algebraic in the statement of PeterzilStarchenko 
Apr
20 
comment 
What is the precise relationship between ominimal theory and Grothendieck's “Esquisse d'un programme”?
non, complex algebraic! I'll edit! 
Apr
20 
awarded  Revival 