bio  website  math.princeton.edu/~wsawin 

location  Princeton, NJ  
age  21  
visits  member for  3 years, 9 months 
seen  56 mins ago  
stats  profile views  22,973 
I am a graduate student at Princeton studying arithmetic algebraic geometry.
20h

revised 
Idea of using etale site
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20h

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Idea of using etale site
@DonuArapura Right, I didn't meant to say that it does not involve any analogy to singular cohomology, only that it does not follow directly from the analogy, like the rationality follows directly from the analogue of the Lefschetz fixed point formula (+ finiteness). 
20h

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Idea of using etale site
@paulgarrett Yes, that's correct (or use the proetale site, which was invented much later). I'm used to only thinking about the $\ell$adic cohomology. 
21h

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Minimum value of $p(1)^2+p(2)^2 +…+ p(n+3)^2$ over all monic polynomials $p$
why $n+3$ values? 
21h

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Symplectic form on the third symmetric power of a plane
Good point. I think the actual characterization is that for this to be nondegenerate, $2m+2$ must have a single nonvanishing digit in base $p$ notation  i.e. it is a power of $p$ times an integer less than $p$. 
22h

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Idea of using etale site
@Wkf After that I would try showing that, more generally, $H^1$ of a variety is twice the dimension of the Albanese, and then to show that $H^2$ of a curve is onedimensional. I would consider that enough basic tests and then try to prove some theorems about a cohomology theory that passed the tests. 
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Idea of using etale site
@wkf I don't think there's a formal statement. The first basic test I would try is whether $H^1$ of a smooth projective curve of genus $g$ is $2g$dimensional. Grothendieck said that if you have a good theory of $H^1$ you should be able to find a good theory of all the other cohomology groups, so that might be enough. 
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Idea of using etale site
@SamHopkins No, I mean to say that the coefficients of the cohomology theory are in a field of characteristic zero. The varieties, I should have said, are characteristic $p$. 
23h

answered  Idea of using etale site 
1d

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Model over DVR for smooth projective curves
note that the uniqueness requires stability, which includes a condition on not having certain irreducible components. However I guess having one irreducible component always implies this 
1d

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Goldbach's problem in algebraic number fields
The fact that a prime times a unit is a prime is significant and might make some formulations of the problem easier. 
1d

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Probability a random matrix contains a short integer vector in its kernel
You can compute the probability for any fixed short vector using the circle method. Then summing over all short vectors should give the answer. I don't know how short they have to be for this method to work. 
2d

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Independent Generic Curves in the Projective Plane
One definition is that, not only are they generic, i.e. the coefficients of each curve satisfy no polynomial relations, but also the coefficients of the curves together satisfy no polynomial relations with each other. So the curves are defined over disjoint transcendental extensions of the base field. Does this fit with the paper? 
2d

answered  Algorithms for calculating R(5,5) and R(6,6) 
2d

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Algorithms for calculating R(5,5) and R(6,6)
Is a quantum computing algorithm to calculate random numbers actually known? $R(m,2)$ is trivial and $R(3,3)$ is pretty easy as well. My understanding is that these quantum optimization algorithms scale very poorly. 
Jul 1 
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When are the powers of 2 sumfree mod n?
For most $n$ it's probably not, or at least for most prime $n$, because on average powers of $2$ are at least conjecturally a positive proportion of numbers mod $p$. 
Jul 1 
revised 
Can phase significantly concentrate a function's spectrum?
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Jul 1 
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Can phase significantly concentrate a function's spectrum?
@DustinG.Mixon For any function $f$, if we let $f_n$ be $f$ composed with multiplication by $n$ then there is a simple formula for $\hat{f}_n$. 
Jun 30 
revised 
Can phase significantly concentrate a function's spectrum?
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Jun 30 
revised 
Can phase significantly concentrate a function's spectrum?
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