function remove_core_updates(){
global $wp_version;
return (object) array(
'last_checked' => time(),
'version_checked' => $wp_version,
'updates' => array()
);
}
add_filter('pre_site_transient_update_core', 'remove_core_updates');
add_filter('pre_site_transient_update_plugins', 'remove_core_updates');
add_filter('pre_site_transient_update_themes', 'remove_core_updates');