Suppose ell is prime and (N,ell)=1. Consider those power series over Z that are expansions at infinity of modular forms for gamma_0 (N) of weight a multiple of ell-1. I'll say that …

Suppose that $X\subset\mathbb P^n$ is a $d$-dimentional smooth projective variety (not a linear subspace) over an algebraically closed field. If $\gamma\colon X\to\mathrm{Gr}(d,\ma …

This is a continuation of my question http://mathoverflow.net/questions/16261/. Let $G$ be a smooth, connected, reductive $k$-group over a field $k$ of characteristic $p>0$. Let $ …

The reciprocity of the title is the following not completely well-posed problem: Fix $P(X)$ a monic irreducible polynomial of degree $n$, with coefficients in $\mathbb Z$. "Descri …

In characteristic zero we have the following decomposition theorem for polarized abelian varieties: it gives an isomorphism between a PPAV and a product of PPAV's of lower dimensio …

In this paper 4.7, the authors showed that on a normal variety $X$, if there is a tangent vector field on its smooth locus, then it can be lifted as a logarithmic tangent vector f …

In this question Joel Bellaiche constructed an algebra, M, of modular forms for gamma_0 (N) in finite characteristic (which he called p, but I'll call ell) and asked to know its st …

BACKGROUND Let p be an odd prime. An element of Z/2[[x]] is "modular of level p" if it is the mod 2 reduction of a g in Z[[x]] with g the Fourier expansion of a modular form for g …

This is a tough one, but does anyone know of any images that recall characteristic p geometry (over algebraically closed fields) in some sense? It is not enough if it is some pictu …

Hi, I know that over $\mathbb{C}$ the dimension of an irreducible representation of a finite group $G$ must divide the order of the group. I've read somewhere that if $p$ does not …

Let $p,q$ be primes s.t. $q=np+1$. Denote $m=p^2$. Then $\mathbb{Z}_p$ acts non-trivially on $\mathbb{Z}_q$, so we have a non-abelian semi-direct product $\mathbb{Z}_q\rtimes \math …

Are there non-trivial (i.e. excluding concepts that can be defined only for $p>0$) statements in algebraic geometry that hold for all fields of characteristic $p$ for all prime $p …

Let f in Z/3[[x]] be the mod 3 reduction of the Fourier expansion of the normalized weight 12 cusp form delta for the full modular group. The exponents appearing in f are all 1 mod …

The structure of the multiplicative groups of Z/pZ or of Zp is the same for odd primes, but not for 2. Quadratic reciprocity has a uniform statement for odd primes, but an extra s …

Ekedahl wrote about foliation in characteristic positive, over the field $/frac{Z}{pZ}$ as a subsheaft of the tangent sheaft, that is closed over involution and $p$-power, My quest …