In order for a PDF file to be displayed it must first be saved on the local computer. That can't be avoided.
What sometimes happens is that the browser saves the file into a temporary folder and then opens it automatically, so you're not prompted to save it in a specific folder. That depends on the settings of each browser.
If there is no way to change it, can I change which folder it adds a copy in? I don't like that it it making a copy in my Documents folder.
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Here, for instance, is the instruction for changing the download location in Chrome. Download a file - Computer - Google Chrome Help
You'll find similar instructions for other browsers if you search Google for "change download location [browser name]".