I believe in most countries only a court can decide if a site is illegal or not. Not you. And as far as I know this is true in both France [0] and Germany[1].
Each arXiv paper has a well-defined license linked-to from the upper right hand corner "(license)" link below the PDF and source downloads. If they only re-hosted and re-compiled papers for which they have a license to do so, I wouldn’t complain at all, but re-hosting and modifying content without a valid license is clearly illegal, no?
> re-hosting and modifying content without a valid license is clearly illegal, no?
No.
Longer version: it's illegal only if a license is required, which is a matter of the copyright law of the jurisdiction relevant to the act. In the US, that question may turn on things like fair use analysis, which can be tricky.
Fair use applies to citations (not of the whole work), parodies and similar creative processes. Similar requirements in Germany include some creative input by the person claiming fair use which usually should exceed the creative content taken from the original work. Simply re-compiling the LaTeX source is certainly not creative work sufficient for a fair use exception. Checking the other limits of copyright law in e.g. Germany ( https://de.wikipedia.org/wiki/Schranken_des_Urheberrechts ) nothing remotely applies to this site.
Could you clarify why you think that this site does not require a valid license to re-host and re-compile papers?
> Fair use applies to citations (not of the whole work)
Time-shifting is one of many examples of where copying a whole work was found to be fair use; the idea that fair use applies only to citations is very, very wrong.
Fair use is extremely precedent dependent (and very hard to predict without clear applicable precedent) because the statute law gives only factors to weigh in the analysis.
> Could you clarify why you think that this site does not require a valid license to re-host and re-compile papers?
I didn't state an opinion on that; I said that, because it skips the question of whether license is required, the blanket statement that rehosting without a valid license is “clearly illegal” is inaccurate and overbroad.
IANAL.
[0] I got the impression it was a French site
[1] just guessing where you live