# Tagged Questions

**4**

votes

**0**answers

131 views

### Partial differential Equation over characteristic p

I want some references on partial differential equations over characteristic $p$. If we have a first order partial differential equation, how can we check whether there exists polynomials or rational ...

**2**

votes

**2**answers

212 views

### irreducible polynomials on the polynomial sequence

I suspect this problem is very famous and it must be studied very well. But I searched in Google and I did not find good reference. I will appreciate any answer and reference for any contribution ...

**5**

votes

**1**answer

374 views

### More expanders?

Having received several exhausting answers to my recent question about
the expansion properties of a certain graph, I now wonder whether anything is
known on the following graphs of a similar nature:
...

**11**

votes

**2**answers

364 views

### An expander (?) graph

For a prime $p$, consider the graph on the vertex set ${\mathbb F}_p$, in
which every vertex $z$ is adjacent to $z\pm 1$ and also to $z^{-1}$ (unless
$z=0$). I was told that this graph is known to be ...

**5**

votes

**3**answers

346 views

### Source for embedding multiplicative group of an algebraic closure of a finite field?

It's easy to embed the (cyclic) multiplicative group of a finite field into the multiplicative group of $\mathbb{C}$ (or other algebraically closed field of characteristic 0): assign to a generator of ...

**1**

vote

**0**answers

153 views

### reference-request for connection between numerator of zeta-function and characteristic polynomial of Frobenius on hyperelliptic curves over finite fields

Let $H$ be a hyperellipitic curve of genus $g$ defined over
$\mathbb{F}_q$. The Frobenius endomorphism operates on the divisor class
group of $H$ and satisfies a characteristic polynomial ...

**6**

votes

**1**answer

585 views

### Exponential sums over finite fields with even characteristic

I am looking for an elementary evaluation (if one exists) of the exponential sum
$$
G_r(a,b) = \sum_{x \in \mathbb{F}_{2^r}} \psi(ax^2 + bx),
$$
where $a,b \in \mathbb{F}_{2^r}^*$ are both units, ...

**7**

votes

**1**answer

705 views

### étale cohomology with G_m coefficients

Most calculations of étale cohomology in Milne's book deal with constructible or torsion sheaves. Are there references where the cohomology of varieties with $\mathbf{G}_m$ coefficients are ...