How to check an ajax nonce in PHP

As of 4.1.1, the nonce is defined in wp-includes/media.php, line 2883:

$settings['post'] = array(
    'id' => $post->ID,
    'nonce' => wp_create_nonce( 'update-post_' . $post->ID ),
);

So to verify the nonce:

wp_verify_nonce( $nonce, "update-post_$post_ID" );