Books can be seen on my kobo on ADE when connected to the computer but not when not connected

Hello,

I've been able to download many books on my kobo but now, when i connect my kobo on the computer and ADE and when i drop a book which is on ADE into my kobo, it says that the book is already on it. When i unplugg my kobo, the book is not on it, eventhough i synchronize it.

It's a new computer on which i've dowloaded without problem ADE (all my books are on it). To make sure, i've unauthorized it and authorized it again, but nothing changes !!

Any idea ?

Thanks in advance.

Best regards.

Agnès