Upload in background in IOS

Ah ! forgot ! with Core API on iOS, from my test Core API for iOS stops sending bytes as soon as the app comes in the background ...

The iOS Core SDK itself doesn't handle running in the background, so you'll need to implement that in your app if you need it. You'll want to refer to Apple's iOS documentation for managing background tasks:

https://developer.apple.com/library/ios/documentation/UIKit/Reference/UIApplication_Class/index.html#//apple_ref/doc/uid/TP40006728-CH3-SW76

mmmm you're telling me that the official Dropbox app IOS does not use the same API ?

The iOS Core SDK is just a wrapper that provides functions for accessing the Dropbox Core API. If you need to run tasks in the background, you can do so in your app, and utilize the SDK to make the API calls. (The official Dropbox for iOS app does use the SDK and implements background functionality as necessary like this.)