799 reputation
410
bio website
location Cambridge, MA
age 25
visits member for 3 years, 9 months
seen Sep 26 '13 at 18:34
I'm interested in topology, algebraic geometry and number theory.

Jun
26
awarded  Yearling
May
10
awarded  Nice Answer
Apr
29
asked A nice rigid analytic model for local systems over an elliptic curve?
Apr
24
comment What is a higher derived constructible sheaf
@David So it sounds like you're saying (in the algebraic case), that the 'etale topos contains all the topology of a manifold up to some sort of profinite completion, and higher-category analogues of locally constant (resp. constructible) sheaves are well-approximated by sheaves on this topos on the one hand, and therefore by D-modules on the other hand. Is this correct?
Apr
23
accepted What is a higher derived constructible sheaf
Apr
23
comment What is a higher derived constructible sheaf
Thanks! This is great. Looking at Aaron Smith's website, I saw he's working on a paper with Block on a constructible Riemann-Hilbert correspondence.
Apr
23
revised What is a higher derived constructible sheaf
minor edits + added local-systems tag
Apr
23
asked What is a higher derived constructible sheaf
Apr
16
answered Algebraic machinery for algebraic geometry
Apr
13
comment Intuition for Levi-Civita connection via Hamiltonian flows
Thank you! I looked at the paper. In terms of its notation, are you saying that the horizontal section is the 1-eigenspace of the derivative of the fundamental endomorphism?
Apr
13
comment Intuition for Levi-Civita connection via Hamiltonian flows
Thanks! Yes, this is exactly what I need. Do you have a link for Foulon's thesis?
Apr
13
accepted Intuition for Levi-Civita connection via Hamiltonian flows
Apr
12
asked Intuition for Levi-Civita connection via Hamiltonian flows
Apr
12
answered Description of the units of the group ring Fp[Fp] ?
Mar
29
comment How much of a variety can be reconstructed from codimension-zero data?
Thanks Sasha! Neat. I agree that when coherent cohomology is trivial, we get no information. However are you sure that there's no data if only $H^n(O)=0$? For example what if we compose your first map with the multiplication map $Hom(O_X,O_S)\otimes Hom(O_X, O_S)\to Hom(O_X, O_S)$ to get a map $Hom(O_X,O_S)\otimes Hom(O_X,O_S)\otimes Ext^n(O_S,O_X)\to Ext^n(O_X,O_X)$. Then if $H^n(O_X)=0$ then this product will of course be zero, but there will be a well-defined and possibly nonzero Massey product. Is it clear that this Massey product will be zero?
Mar
29
accepted How much of a variety can be reconstructed from codimension-zero data?
Mar
26
awarded  Nice Question
Mar
26
comment How much of a variety can be reconstructed from codimension-zero data?
Hm... I agree that it seems like something is lost in dimension $>1$, but not sure your argument is correct, or else I'm not following it. On a curve, if you take the extension closed abelian subcategory of $(D^b)Coh(X)$ generated by $O_X$ and all structure sheaves of points, you get all of $Coh$, which certainly lets you recover $X$. So despite the fact that Homs and Exts between objects in the subcategory <i>consisting</i> of $O_X$ and skyscraper sheaves depend only on the coherent cohomology, once you start taking extensions things can become more subtle. How does Hartog change this?
Mar
24
awarded  Commentator
Mar
24
comment How much of a variety can be reconstructed from codimension-zero data?
Yes, of course (otherwise it'd be boring in dimension $>1$).