I'd just comment that Paul doesn't go into detail concerning the historicity of Jesus because it was already assumed by his audience. Paul was not a historian or an apologist in our modern conception of the term-

As Ben Witherington said:

"he was a pastoral theologian called upon to deal with matters of theological weight and direct bearing on the issues which arose in the churches." [Ben Witherington, III “Christology” in Dictionary of Paul and His Letters, (InterVarsity, 1993), 109.]

It takes a modern low context mindset to ask that Paul would have in his ancient high context culture include details that were simply not necessary to record. It seems that those of the hyper-skeptical persuasion cannot help but to read Paul's epistles anachronistically.

Oh, and I'd also point out that 90% of Paul's use of the title 'kyrios' (lord) is in reference to Jesus -- it would be special pleading to suggest that Paul could possibly be speaking of 'the Lord God' [the Father] when he mentions the Lord who was crucified. The context of 1Corinthians is far from ambiguous on the referent.

B"H