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 picture that can be also understood solely in characteristic 0.


A quick search through the literature has proved fruitless.


I have been thinking for a while of asking this question, but I never had a pressing need rather than my own curiosity. However, now I am trying to improve a poster by including pictures but the topic is algebraic geometry in characteristic p. 


An example of such an image in Complex Geometry would be the arrangement of contracted and blow up curves in the standard Cremona transformation of the projective plane. The one in this [poster](http://www.maths.ed.ac.uk/cheltsov/cremona/poster.pdf) is simple but effective.


I believe this question also might be of interest for people who try to explain research to non-mathematicians or simply to mathematicians who are not geometers.



Intuitive pictures in characteristic p
I don't think you can draw something meaningful - I would be surprised if someone made a good drawing of the Frobenius morphism ;).


That being said, here is an example (possibly misleading or unrelated to your research) I saw in the slides of Benedict Gross's lectures on the arithmetic of hyperelliptic curves. Take a prime $p$, say $p=57$, and an equation of an hyperelliptic curve $y^2 = x^n + ax^{n-2} + \ldots$ with integer coefficients. Draw a $p\times p$ square and mark the solutions to the above equation mod $p$. The resulting picture exhibits the following:


* It is a mixture of chaos and geometry: there is a visible symmetry coming from the hyperelliptic involution $(x, y)\mapsto (x, -y)$.
* The solutions form a finite set, in particular, it makes combinatorial arguments possible. We can ask how many points are there and whether it gives us some "geometric" information. This is not obvious to someone from other fields, or a non-mathematician.


You can include drawings of the same curve over $\mathbb{R}$ and $\mathbb{C}$. I think the equation $y^2 = \ldots$ and the three pictures together explain pretty well what algebraic geometry is about without going into too much detail.


