A lasting memory?

I find the dichotomy that Supulcius Severus in his first section sets up between memory and life intriguing.  Since the human life is so relatively short, focusing on the here and now does seem to be an effective way to live rather than how you are going to be remembered.  As a Christian writer though, the importance of a pious life and one that follows the doctrine of Christianity is essential as well.  Perhaps I'm misreading, but I wonder if the focus on eternal life rather than eternal memory also touches on the Christian concept of heaven, in that your life (vita) will continue, just not on the earthly sphere.  I do not think though the living a good life and leaving behind a good memory of yourself are not mutually exclusive, but rather seeking the former is far more important than the latter.