Reputation
7,958
Next privilege 10,000 Rep.
Access moderator tools
Badges
31 52
Newest
 Enlightened
Impact
~215k people reached

2d
comment Rationally connected spaces over non-algebraically-closed fields
@AntoineDucros If $X$ is a conic, then the second projection $p_2$ gives $X\times X$ the structure of a Severi-Brauer scheme over $X$, and since it has a section (the diagonal), it is isomorphic to $\mathbf P^1\times X$.
Apr
22
comment Reduced scheme and closed points
@AdamTopaz Could you please precise what this "standard trick" is exactly? Thanks!
Apr
22
comment Non-Archimedean non-standard 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
comment 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
comment 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
comment Examples of common false beliefs in mathematics
@Michael Wasn't it the sum of the empty set of half-roots 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
comment 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
comment What is the precise relationship between o-minimal theory and Grothendieck's “Esquisse d'un programme”?
@EmilJeřábek Thanks for the correction. I edited accordingly.
Apr
21
awarded  Enlightened
Apr
21
comment Examples of common false beliefs in mathematics
I meant that $V-U$ 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
comment 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
comment 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
comment 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 o-minimal 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 o-minimal 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 o-minimal geometry. At least not obviously.
Apr
20
revised What is the precise relationship between o-minimal theory and Grothendieck's “Esquisse d'un programme”?
add: complex algebraic in the statement of Peterzil-Starchenko
Apr
20
comment What is the precise relationship between o-minimal theory and Grothendieck's “Esquisse d'un programme”?
non, complex algebraic! I'll edit!
Apr
20
awarded  Revival