[_flag]

I solve 034.

By [1, Theorem 4.1], the Neron-Severi rank of the perfectoid cover is the same as the Neron-Severi rank of the reduction. For a product E x E' of elliptic curves, it is well known that NS(E x E') = NS(E) + NS(E') + Hom(E,E'); see [2, Prop. 2.3]. Since E = E' here and E is supersingular, this number is 1 + 1 + 4 = 6.

Is it research level? It of course takes a graduate student a long time to understand, say, what a perfectoid space is. But the statement follows immediately from quoting the literature, as long as one knows what to quote.

1. https://arxiv.org/pdf/2105.05230 2. https://arxiv.org/pdf/1402.2233

[christianstump]

You see yourself that your own solution is purely of theoretical nature and not at all what you wrote before, right? (And no, I am not commenting on your answer.)

[_flag]

Indeed. But I chose the problem in response to your comment:

> But we give no indication that the questions are hard because of computational tasks and we give many indications that the problems are of theorecical nature and hard for theoretical reasons.

and Question 034 seemed to be one of the few that did not have a computational component, and so would presumably be hard for theoretical reasons. I already indicated above some problems that I feel to be of a non-theoretical nature.