Some say the Torah was written much later, most likely during the Babylonian exile.
However, the Torah couldn’t possibly have been written after the split between Israel and Judah. They each got their own slightly different Torah, which suggests it was written before the split, and then diverged in each community. Neither has the power to “correct” the other.
We need to look at who wrote the Torah, or Pentateuch, then at when each section could have been written. Tradition says that the Torah, with all its contradictions and inconsistencies, was written by one man, Moses, around 1400 BCE, but this is clearly not the case.
In the nineteenth century, Julius Wellhausen carried out stylistic analyses, and was able to assign authors called J (the 'Yahwist') and E (the 'Elohist') to the nature and fertility stage of religion, D ('Deuteronomist') to the spiritual and ethical stage, and P ('Priestly Source') to the priestly and legal stage. At the same time, historical analysis suggested that J was the earliest source, E somewhat later, and D and P centuries later than J.
Some modern scholars suggest modifications to Wellhausen's hypothesis, but almost all are in general agreement. The consensus is that the Yahwist wrote in around the ninth century BCE; the Elohist in the eighth century BCE, but definitely before the fall of Israel in 722 BCE; the Deuteronomist in the seventh century BCE and the Priestly Source during or shortly after the Babylonian Exile. These writings were then redacted into more or less the form we know today, by the Redactor. The redacted compilation is definitely post-Exilic and so belongs to the period around the fifth century BCE.
Only the Elohist wrote in the northern kingdom of Israel, and this writing was redacted, shortly after the fall of Israel and the influx of refugees from Israel to Judah, into the writings of the Yahwist, who had written from the perspective of the southern kingdom of Judah. The Samaritan Torah represents an early post-Exilic version of the Judahite books, not a continuation of some pre-722-BCE set of books.
You write,
However, Torah couldn't possibly be written before the split between Israel and Judah. They each got their own slightly different torah. Neither have power to "correct" the other.
I disagree. The fact that both Israel and Judah have their own slightly different version of the Pentateuch is actually evidence that the Pentateuch was written before the split, and changed slightly by one or both groups through the years. However, this split need not be the split between Israel and Judah after Solomon, but may simply be any point in time at which the Pentateuch came under the protection of two independent groups of people with different religious convictions (i.e. Jews and Samaritans).
The discussion of when and how it was compiled is long and complicated, with many strong and weak arguments on either side. Modern scholarship is very divided. In the words of Wikipedia,
Today the majority of academic scholars accept the theory that the Torah does not have a single author, and that its composition took place over centuries. From the late 19th century there was a general consensus around the documentary hypothesis, which suggests that the five books were created c. 450 BCE by combining four originally independent sources, known as the Jahwist, or J (c. 900 BCE), the Elohist, or E (c. 800 BCE), the Deuteronomist, or D, (c. 600 BCE), and the Priestly source, or P (c. 500 BCE).
This general agreement began to break down in the late 1970s, and today there are many theories but no consensus, or even majority viewpoint. Variations of the documentary hypothesis remain popular, especially in the United States of America and Israel, and the identification of distinctive Deuteronomistic and Priestly theologies and vocabularies remains widespread, but they are used to form new approaches suggesting that the books were combined gradually over time by the slow accumulation of "fragments" of text, or that a basic text was "supplemented" by later authors/editors.
The fact that there are so many different views, even amongst those who agree on that the Pentateuch developed over centuries and is the result of many different authors' hands, there is significant divergence. So we have two choices: either we believe by faith the vast majority of the Pentateuch is the work of a single author, as indicated by the New Testament, and find ways to resolve apparent inconsistencies in it. Or we ascribe to one of the dozens of "redaction" theories, which have the advantage of making apparent inconsistencies acceptable, but have the disadvantage of being, to a large extent, based on speculation seeking evidence.
Much more could be written about the authorship of the Pentateuch. Indeed, much more has been written. Happily, one doesn't need to be a scholar to make an informed decision: critically considering the strongest arguments of each side should suffice.
I know of no scholar who says the Torah was actually written after the Babylonian Exile. Many, however, believe it was combined from several earlier sources and finally reached the form it now has at that time.
The basic idea here stems from the documentary hypothesis first promulgated in the 19th century. The theory identifies four main sources:
Scholars associate "J" with the southern Kingdom of Judah around the ninth century B.C.E., and "E" with a more northern context slightly later. "P" and "D" were written several centuries after this and a redactor, "R" compiled the book into what we have today in the fifth century BCE. link to source
The OP refers to Northern and Southern Israel each having a slightly different version of the Torah. I suspect this idea confuses the Samaritan Pentateuch with the Torah. The Northern Kingdom of Israel is not the same as Samaritan kingdom which probably produced its version of the Torah several centuries later. The Samaritans did not recognize the legitimacy of either Judah or Israel. It is possible that the northern kingdom did have its own version of the Torah, but we do not know if and how it differed from the southern version.
To summarize the answer to the main question: the documentary hypothesis holds that the Torah was written over several centuries, starting sometime after Solomon's reign, with the various strands being combined over stages until they reached their present form sometime after the Babylonian exile.
I would like to combine what I understand from Dick and Niobius answer. Niobius seems to be from "christian" perspective and suggest earlier date. Dick seems to propose latter date.
Basically both agree that the whole 5 books must have been written before the "split" between Judah torah and Samaritan torah.
The difference is when the spit is and what the split is. Am I getting this correct?
The split does not necessarily the split after Solomon rule (around 850 BCE?). It could be that after the northern israel kingdom is defeated and conquered by Assyrians, refugees would go to norther israel, copy torah, and create the split.
And we don't know which one.
So this will be a base for another question.
One bit of evidence is that the Jewish community at Elephantine, which was founded pre-exile, appears not to have had the Torah based on the absence of any knowledge of the Torah in their documents from the 4th century BCE (see page 49).
There doesn't appear to be any good reason for late dates for the Old Testament of the Bible (at least for the Torah/Pentateuch) since many of the people names, place names and events have been confirmed as having existed through extra-Biblical sources. Among these are Abraham, Noah's son Japheth, the 4 kings who fought against Sodom and Gomorrah (Chedorlaomer, Amraphel,Arioch and Tidal - all mentioned on a single clay tablet from that era) and others too numerous to mention. Joseph's image recently discovered on gold coins from Egypt in the correct era as well. Later kings - Hezekiah, Jehu, Joram. The list goes on. Perhaps the scrolls were collated later but any thought that they were later inventions by later scribes is rapidly becoming untenable as more and more of the so-called myths are being shown to be actual events/people/places.
