35,955 reputation
258133
bio website math.princeton.edu/~wsawin
location Princeton, NJ
age 21
visits member for 3 years, 10 months
seen 5 hours ago

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 Deligne-Mumford 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 $\{x-a:0\leqslant a\leqslant z-1\}$
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 quasi-finite?
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 Galois-invariant 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 Calabi-Yau 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 $i \geq (g-1)/2$ 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