It kinda has to be the permalinks setting in your WordPress admin though.
Not sure which method you used to transfer your database. If you did an export (on local) and then import (on server) both through PHPmyadmin, it should have gone right. However if you did it within the WordPress admin, it’s very likely you only transferred the CONTENT and not a bunch of SETTINGS (including the permalinks setting).
You could try uploading your local .htaccess file to your server, that helps sometimes. Or check if the URLs (WordPress URL and Site URL) are correct — you may have to get rid of the “/wordpress” part in one of them or both.