I use a home NAS for this, accessing the files from both devices. maybe that could work for you.
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Dolphin (and I'm sure other file browsers) has a couple sync plugins. Like gdrive, mega, idrive and a few other.
Syncthing is probably the best option. It'll keep a copy on both devices, and can sync any changes made on any device. It's a direct connection, no intermediary server required.
Another way, which is a bit round-about, but surprisingly easy: Install Zim Desktop Wiki (a notebook app), enable its built-in web server, and add your PDF to the Zim notebook. From the iPad use the web browser to open your Zim notebook (Assuming both are on the same wi-fi). This is read-only from the iPad, can't make changes.
Im using resilio sync and secure shell fish.
There's a syncthing wrapper for iOS (Möbius Sync), which is free up to 20 MB of synced files. The unlimited version only costs $5 once, so might be worth it.
Otherwise I'm sure there's ways to set a network fileshare on your PC, that you can access from your iPad (if you only need it in LAN).
Thanks! I am trying it out, and it is working great so far!
Use syncthing, there is some unofficial app on the iPad for it and the official one on Linux.