To download the ArcObjects SDK for .Net or Java log into to customers.esri.com. Click the icon for software download. Under Product line if you are eligible for ArcGIS Desktop you should see ArcGIS for Desktop in the Product line, click hyperlink for ArcGIS for Desktop. This will take you to a new page where under Download Individual Setups you will see ArcObjects SDKs, you can expand that to select either .NET or Java.