# Tagged Questions

321 views

### When are arithmetic and geometric monodromy equal?

Let $f: Y\to X$ be a finite separable morphism of curves over the finite field $\mathbb{F}_q$. Is there a simple condition under which the arithmetic and geometric monodromy of the covering are equal ...
381 views

### Equations of elliptic curves

First part of question I have asked on mathoverflow already: http://math.stackexchange.com/questions/467088/explict-form-of-the-equation-of-elliptic-curve 1) Let $E(\mathbb{F}_{q^2})$ is elliptic ...
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### Does the Hilbert polynomial determine the weight of the Galois representation associated to a variety

Let $X$ be a curve or an abelian variety (over a finite field). Then the Galois representation associated to $X$ via the etale cohomology of $X$ (in degree $1$) is integral of weight $1$ and its ...
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### Number of solutions to $mx^2+ny^2 \equiv k\pmod{p}$

I need a reference for the result which gives the number of solutions to the congruence $mx^2+ny^2 \equiv k\pmod{p}$. This result seems to be something that would be discussed in Gauss' ...
I was told that Weil reciprocity theorem (one has two meromorphic function $f,g$ on a complex curve $C$, so $\prod\limits_{x\in C} g(x)^{ord_xf}=\prod\limits_{x\in C}f(x)^{ord_xg} \$ where $ord_xf$ ...
Let $k$ be a finite field. We define $N(d,g)$ to be the number of plane curves $f(x,y)$ defined over $k$ of degree $d$ with (geometric) genus $g$. If $D(d) := (d-1)(d-2)/2$ (the maximum possible ...