bio  website  math.princeton.edu/~wsawin 

location  Princeton, NJ  
age  21  
visits  member for  3 years, 10 months 
seen  5 hours ago  
stats  profile views  23,506 
I am a graduate student at Princeton studying arithmetic algebraic geometry.
2d

comment 
Coherent cohomology of the moduli space of curves
@JasonStarr I think that the main Weil cohomology theories all behave the same for smooth proper DeligneMumford stacks but I'm not completely sure. I'd be happy to hear the answer to that question as well! 
2d

comment 
Do modular forms show up in the cohomology of moduli spaces of unmarked curves?
Interesting! I'll look into this... 
Jul 30 
reviewed  Leave Closed system with solutions $\{xa:0\leqslant a\leqslant z1\}$ 
Jul 30 
comment 
What's the relationship between the different versions of the BBD decomposition theorem?
I don't think $\chi$ must have finite monodromy. Do you mean that the local monodromy is quasifinite? 
Jul 30 
asked  Coherent cohomology of the moduli space of curves 
Jul 29 
comment 
Do modular forms show up in the cohomology of moduli spaces of unmarked curves?
@JasonStarr I just expect that whichever kind of chern numbers are easy to calculate are also the kind that have the right behavior under finite etale covers. But the arithmetic Euler characteristic of a stack does not have the right behavior under finite etale covers. I might ask an MO question just about this... 
Jul 29 
comment 
Do modular forms show up in the cohomology of moduli spaces of unmarked curves?
@JasonStarr Does this give you the right answer for stacks? If you try it for $\overline{\mathcal M}_{1,1}$, won't you get $1/12$ or $11/12$ or something? 
Jul 28 
comment 
Pure motives and compatible systems of $\ell$adic representations
@Rex. $\pi$ is a Galoisinvariant class on $X\times X$. Viewing cohomology classes as endomorphisms, the Galois action is by conjugation. So the conjugation action is trivial and so $\pi$ commuters with all elements of the Galois group, including Frobenius. 
Jul 28 
revised 
Counting subspaces
added 1250 characters in body 
Jul 28 
reviewed  Reopen Recent progress on the busy beaver problem? 
Jul 28 
comment 
Flat cohomology of an ordinary liftable CalabiYau threefold
This seems false, because the Picard group might be $\mathbb Z$, in which case your formula shows that the cohomology group is $\mathbb Q_p/\mathbb Z_p$. 
Jul 27 
revised 
Counting subspaces
added 174 characters in body 
Jul 27 
revised 
Counting subspaces
added 174 characters in body 
Jul 27 
awarded  Nice Question 
Jul 27 
comment 
Do modular forms show up in the cohomology of moduli spaces of unmarked curves?
@ulrich I don't know. I checked to see if it is known to be zero, in which case this would be quite a silly question, and I could not find any evidence either way. Maybe that would be a better question then this one. Can $\chi_a( \overline{\mathcal M}_{g})?$ possibly be estimated? 
Jul 27 
comment 
Counting subspaces
I'll post an edited version soon. 
Jul 27 
comment 
Counting subspaces
@the_fox Yes, that's not right. I wrote down the subspaces you have to avoid wrong. In fact there is no simple product formula. However if you fix the dimension of the intersection the $k$dimensional subspace with $W_1 \cup W_2$ you get a product formula. So you have to sum over all these products. 
Jul 27 
comment 
Do modular forms show up in the cohomology of moduli spaces of unmarked curves?
@JasonStarr Yes, I think so. So we need to take $i \geq (g1)/2$ for the left side to be nontrivial. The right side can be nontrivial for $i$ all the way up to $2g$. 
Jul 26 
reviewed  Leave Open Extending an homotopy, knowing the two base functions extend 
Jul 26 
reviewed  Leave Open Class forcings and elementary embeddings 