26,967 reputation
24098
bio website math.princeton.edu/~wsawin
location Princeton, NJ
age 20
visits member for 2 years, 11 months
seen 3 hours ago

I am a graduate student at Princeton studying arithmetic algebraic geometry.


Aug
16
comment Points on the intersection of an affine quadric and cubic over a finite field
What you want may relate to Chevalley's theorem: en.wikipedia.org/wiki/Chevalley%E2%80%93Warning_theorem
Aug
16
comment Does this “modeling relationship” occur in mathematics (Galois connections, relation algebra, category theory)?
I don't think modeling relationships form a category because there is no way to compose them and no natural identity element.
Aug
13
answered Preimage of smooth curves under morphism of smooth varieties
Aug
12
answered Proofs of the Chevalley-Warning Theorem
Aug
10
answered Interpretation of $H_1(A_\mathbb{C}^{top},\mathbb{Q})$
Aug
10
comment support of embedded points in a curve
$l_p$ is necessarily a singular point of $C$....
Aug
6
comment Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
Because it counts solutions to the equation $x = E(x)$ where $E$ is multiplication by $\sqrt{-D}$. For each such $x$, $(x,x)$ is a transverse intersection point of the two curves.
Aug
6
answered Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
Aug
6
awarded  Enlightened
Aug
6
awarded  Nice Answer
Aug
5
comment If a graph invariant is NP-Hard, is its “deck ratio” NP-Hard as well?
I don't understand your example $\phi_1$. If $G$ has an even number of vertices, then $\phi_1(G-v)=-1$, right? So the deck ratio is just minus $\phi_1$. So how can one be NP-hard and the other NP-easy? I think it might be sufficient to mandate nonzero values.
Aug
4
comment Connections between Standard, Hodge and Tate conjectures on algebraic cycles?
For the Lefschetz conjecture, we need a certain ring to contain a left inverse or right inverse of an element. In other words we are looking for solutions of the equation $XY=I$, for $Y$ defined over $\mathbb Q$. If we have such a solution after tensoring with $\mathbf Q_\ell$, we must have it before tensoring.
Aug
4
comment Connections between Standard, Hodge and Tate conjectures on algebraic cycles?
@ACL: For the Kunneth conjecture, the cycles we are searching for are idempotents in a certain ring. If upon tensoring with $\mathbf Q_\ell$ an algebra has a certain idempotent, then I believe that before tensoring it has corresponding elements whose eigenvalues are in $\mathbf Q_\ell$, that is, they are in an algebraic number field that splits at $\ell$. Combining all $\ell$ I think we get the desired statement. So maybe one needs Tate at each $\ell$.
Aug
2
comment Derived categories of curves equivalent then the curves are isomorphic
Can you get a uniform proof using Torelli's theorem? It says that if two curves have the same integral Hodge structure (including Poincare duality) then they are isomorphic.
Aug
1
answered Cyclotomic character in class field theory
Aug
1
answered Circles avoiding rational points of height $\le h$
Jul
31
comment Escape the zombie apocalypse
As long as area of each sector grows exponentially, the probability of not having any zombies in the sector falls superexponentially. Since the number of segments grows exponentially, by the union bound you're the probability of each segment having a zombie is close to 1.
Jul
31
comment Newton polygons of modular polynomials
I worked out in more detail my thoughts about the bottom corner. I think this is more related to Heegner points of conductor $1$, because these are the CM points associated to split ideals in $\mathbb Z[\omega]$, not in a subring.
Jul
31
revised Newton polygons of modular polynomials
added 1285 characters in body
Jul
30
comment Connections between Standard, Hodge and Tate conjectures on algebraic cycles?
$H^{2i}(X,\mathbb Q_\ell)$ and $H^{2d-2i}(X,\mathbb Q_\ell)$ are dual Galois representations. If we have a cycle class in the first one that gives a cyclotomic subrepresentation, so we get a cyclotomic quotient representation of the other one. I think the Tate conjecture is usually taken to include semisimplicity (or it implies that?), so this gives you a cyclotomic subrepresentation that is dual to the first one.