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location Cambridge, MA
age 26
visits member for 5 years, 2 months
seen Sep 2 at 2:53
I'm interested in topology, algebraic geometry and number theory.

Jul
28
comment Transcendental distance sets
The same sort of argument can be used if you're avoiding any countable collection of algebraic relations.
Jul
28
comment Transcendental distance sets
You can use Zorn's lemma and measure theory. Suppose $S$ is a maximal subset of $\mathbb{R}^n$ with no algebraic volumes - one exists by Zorn's lemma. Let $D$ be the set of all points $z$ of $\mathbb{R}^n$ such that $z$ forms a simplex of algebraic volume together with some $n$ points of $S$. Since the set of $n$-tuples of points of $S$ is countable, and the set of algebraic numbers is countable, you see that $D$ is a union of a countable collection of hyperplanes, thus has measure zero. This means that there is a point in the complement to $D\cup S$, so $S$ is not maximal - contradiction!
Jun
26
awarded  Yearling
May
10
comment When is the Hom-scheme connected?
Whether or not you assume commutativity, you won't in general get connectivity. Take for example maps from the n'th neighborhood of $0$ in $\mathbb{A}^1$ into the n'th neighborhood of $0$ in $Spec(k[x,y]/(xy)$. These mapping spaces are in general at least as complicated as mapping spaces of fixed degree between projective varieties: if $A$ is functions on a neighborhood of the affine cone of a projective variety $X$ and $B$ is functions in a neighborhood of 0 in a veronese twisted affine cone of $Y$ then $Map(B,A)$ goes to $Map(X,Y)$ surjectively by taking blowups of tangent cones.
May
10
answered Fundamental group of the complement homogeneous variety in $\mathbb{C}P^{n-1}$
Apr
27
answered Is there a nonzero sheaf with all cohomologies vanish?
Apr
27
asked Twisting stable maps to C* equivariant space by a line bundle
Apr
5
answered On a theorem of Kazhdan
Mar
25
comment On a theorem of Kazhdan
Ah sorry, thought you were twisting by a character of the Levi (which would not affect the dimension... your current question makes a lot more sense).
Mar
24
revised On a theorem of Kazhdan
minor correction
Mar
24
awarded  Informed
Mar
24
revised On a theorem of Kazhdan
minor edit
Mar
24
answered On a theorem of Kazhdan
Mar
18
awarded  Popular Question
Feb
11
awarded  Self-Learner
Jan
12
revised Twisting of the power functor
minor edit: added the word "perfect" in a couple places
Jan
12
comment Twisting of the power functor
Hi David, I mean the category of perfect modules over $T(k)$, which I think it's enough to consider as a DG algebra over $k$. (Correct me if this doesn't make sense).
Jan
11
revised Twisting of the power functor
edited typo
Jan
11
asked Twisting of the power functor
Dec
1
accepted What is the coefficient ring of algebraic K theory of the discrete $\mathbb{C}$?