It worked! thanks.
For reference, i modified this file : /application/view/omeka/admin/asset/add-form.phtml ; to change the file types allowed on the client side, then the one you said (AssetAdapter) for the server side verification.
Once this is done, it’s still broken because Asset doesn’t have anything to display pdf files, so i did this :
In the file application/view/omeka/admin/asset/browse.phtml
At the line 60
Insert this : <a href=<?php echo $asset->assetUrl(); ?>>Link</a>
This will add the link to the file to each row.