Hi,
As far as i remember JURI::current does not include the query part ( if any ) of the URL.
The variable absoluteURL is build directly from the core API:
$uri = JURI::getInstance();
$item->absoluteURL = $uri->toString();
If it's not working for you, then probably something is wrong in your configuration.
Finally, regarding the Nginx setup you might want to take a look at those resources:
docs.joomla.org/Nginx
docs.joomla.org/Enabling_Search_Engine_Friendly_%28SEF%29_URLs_on_Nginx