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Let $X$ be a smooth scheme of finite type over $\mathbb Q$ or $\mathbb Z$. It is natural to consider $D(X)$, the derived category of coherent sheaves on $X$. Beyond the definition, have there been any …

It is well-known that the compactification $\overline M_{1,1}$ of the moduli space of elliptic curves over $\mathbb C$ is a weighted projective line with weights $4$ and $6$. As far as I can tell, th …

This is pretty much straightforward curiosity. Is there anything known about Newton polygons of classical modular polynomials (polynomial relations between $j(\tau)$ and $j(n\tau)$)? I understand that …

In his work on mirror symmetry (http://arxiv.org/pdf/alg-geom/9502005v2.pdf) Igor Dolgachev has considered families of K3 surfaces of Picard rank at least 19 with the base given by $X_0(n)^+$, the quo …

Has anyone come across anything along the following lines? Let $X_1(p)$ be the compactification of the quotient of upper half plane by $\Gamma_1(p)$ for some unspecified large prime. Let $X_1(p) \to …

This is really more of an extended comment, but it would be unpleasant to write it in that format. I am commenting on the suggestion of Peter Mueller to argue that the boundary of the triangles he con …

Sorry, don't know a reference, but here is a quick argument. If $M=p^ab+c$ with $0\leq c\leq p^a-1$, then $$(1+x)^M=(1+x)^{p^ab}(1+x)^c =(1+x^{p^a})^b(1+x)^c \mod p. $$ In turn, this equals $$ (1+bx …

Has anyone successfully defined and studied analogs of vertex algebras where the grading of the fields is by $(\log \mathbb Q)$ rather than $\mathbb Z$? What I mean is that the usual fields $$ a(z) = …

In algebraic geometry there are examples when a variety $X$ is somehow related (I call it double-mirror) to another variety $Y$, together with a 2-torsion Brauer class. By "related" I mean statements …

The solution set $L$ is clearly a sublattice in $\mathbb Z^d$. If $a$ is fixed and $N$ grows, the number of lattice elements in a box grows approximately as $cN^{rank}$. So if you have your statement …

Suppose I have a curve $C$ defined over $\mathbb Q$ and a line bundle $\mathcal L$ on it, also defined over $\mathbb Q$. I am interested in trying to find a (non-effective) divisor $D=\sum_i a_ip_i$ o …

Just a simple proof of the formula for $2$ and $10$. The remainder modulo $8$ is unchanged under the operation $f$, since $2^k=10^k$ modulo $8$. On the other hand, you will never reach $0$ or $1$ if y …

I am reading the paper of Gross and Zagier on heights of Heegner points and would like to check with the experts whether the following (meta?)mathematical statement makes sense. In the calculation of …

What is knowns about Weierstrass points on modular curves? Are there any explicit formulas of them, or any information about Weierstrass gaps? I am interested in (compactifications of) the quotients o …

There are in fact explicit equations (at least for the prime level) worked out in arXiv:math/0010272.