What are the 'Scriptures' mentioned in 1 Corinthians 15? What are the 'Scriptures' mentioned in 1 Corinthians 15: 3 - 4?

. . . Christ died for our sins according to the Scriptures.
. . . He rose again the third day according to the Scriptures.

If Paul called something 'scriptures' I would like to know what it was and take his opinion seriously.
Did the Corinthians have the same Bible we have?
Did they have access to 'Scriptures' other than the modern Bible?
Did Paul teach from the same 'Scriptures' they had?
As a "Pharisee amongst Pharisees," Paul would have seen the Scriptures as the Scriptures of the Jews - the Torah, the Ketu'vim, and the Nevi'im, or as we say in English, the Law, the Writings, and the Prophets. When Jesus was on the transfiguration mount, he prefigured this. These Scriptures are the Old Testament to modern Christians, or "the Hebrew Bible" as some scholars like to say.  


Dead for three days, in the OT Scriptures

When Paul was speaking of Jesus, rising again after three days, for example, he was probably remembering what the eyewitnesses had said, and which Matthew later wrote as follows:


  38 Then some of the scribes and Pharisees answered him, saying, “Teacher, we wish to see a sign from you.” 39 But he answered them, “An evil and adulterous generation seeks for a sign, but no sign will be given to it except the sign of the prophet Jonah. 40 For just as Jonah was three days and three nights in the belly of the great fish, so will the Son of Man be three days and three nights in the heart of the earth  (Matthew 12:40)


Here, Jesus explicitly called out Jonah (an Old Testament prophet) as being prophetically foretelling that the Son of Man would also be dead for three days. Paul admits to having been taught by Peter, and Peter would have been privy to this teaching from Jesus himself.
Dying for our sins in the OT Scriptures

Likewise, Paul may very well have read into Isaiah 53 for inspiration about Jesus death paying for our sins, when the prophet writes:


  But he was pierced for our transgressions;
  he was crushed for our iniquities;
  upon him was the chastisement that brought us peace,
  and with his wounds we are healed.
  6 All we like sheep have gone astray;
  we have turned—every one—to his own way;
  and the Lord has laid on him
  the iniquity of us all. ... 10 his soul makes an offering for guilt,


While scholars may disagree on the nature of substitutionary atonement as the "Gospel" that Paul preached, this prophecy could at least be seen to be in harmony with Paul's understanding.
Jesus calling himself the OT Scriptures

While the specific passages may or may not "clearly" be the exact references in question, the overall point is explicit - that Jesus was the fufillment of what the Jews had long believed. Jesus says as much to the Pharisees in John 5:39:


  You study the Scriptures diligently because you think that in them you have eternal life. These are the very Scriptures that testify about me.


Herein the obvious implication is that the Scriptures are those Scriptures that the Pharisees and the religious folk of the day had been searching for centuries. Presented with the Christ who literally was the Word (John 1), it all began to make sense. 


The New Testament, by definition, came after the Hebrew Scriptures and to the Hebrews for whom those Scriptures were written. By definition, the "Scriptures" should mean to those authors what "Scripture" meant to the contemporaries of those authors.  When Paul was writing his letters, there were no "Gospels", only eyewitness accounts, so he couldn't have been referring to anything more. 

Corinth itself, as a port city in Greece, was home to a substantial Jewish population, so there is no reason to assume the word would have meant anything different than what you'd expect a Jew to think it - namely those books we now call the Old Testament.