Yes, the radiocarbon dating says 14th century. So then you have two possible theories, the first is that it is a 14th century forgery. That was the assumption that most of the scientists had when they began.
So then, let us consider this 14th century forger.
1st we assumed that the blood would be chicken or pig, etc. But it was human.
2nd we assumed that the blood would be a different blood type from the Suderian (the odds were 90% that it would be different) but it wasn't, it was the same.
3rd. We assumed that pollen would prove that this relic never left Turin, but instead the pollen showed that it had been in Jerusalem, Turkey, and Constantinople prior to the time for which we have a well documented record of where it was.
4th We were also able to prove that the shroud had once laid on the floor of a limestone cave in Jerusalem. Although limestone can be found around the world, the trace elements in limestone give it a unique fingerprint. Because the only real question concerning the shroud is whether or not it is the actual shroud of Jesus the scientists used that limestone as a comparison and discovered a match.
5th We also assumed the image was made by some kind of paint or dye. It isn't.
6th Some thought that it might have been made by projecting some kind of crude photographic image onto Shroud (14th century predates the invention of photography, but clearly this forger was way ahead of his time). However, this theory was disproved when they discovered that 3 dimensional information is encoded in the image (see the Nova special -- the face of Jesus). That strange elongated face is created when you drape a shroud over a 3d image. When they ran it through the imaging software the result is a much more normal, middle eastern face of a relatively young man.
7th we were able to match the wounds on the back to an actual Roman artifact from the time of Jesus.
8th we assumed we could easily prove the item a forgery based on the textile. This is how many paintings are proven forgeries. However, it has been confirmed to be accurate for a Jewish burial, the material is accurate for the time, and the weave is accurate.
9th we assumed a forger would position the nail holes where you see them in paintings, in the palms, rather then in the wrist. However, the nail holes were accurate and as a result you can see that the nerve connecting the thumb had been severed, which is what you would expect.
10th We found evidence that one knee was swollen, which does correspond to the story of him falling on it while carrying the cross.
11th we also found evidence that the wounds on one shoulder were mashed down which would be expected if you were carrying a heavy weight.
12th We found something very strange, the crown of thorns was not as it is depicted in paintings, but rather a clump of thorns marks all over the head as though they chopped off a bush and stuck it on his head. Forensic scientists always look for the parts of the record that don't match recorded history. The clump of thorns appears much more believable than having some Roman soldier doing arts and crafts at the time of the crucifixion.
13th When you look at the blood pattern from the wrists you can see two distinct blood flows. When we reconstruct it there is a direct correlation to a person hanging from the cross in one, and then pulling themselves up to breath in the second.
14th. Not only do we know that the shroud was in Jerusalem, on the limestone that the tombs are in. But we also know, from the pollen, the time of year, which also matches the account that this happened over the passover. We did find pollen from this very severe thorn bush that grows in Jerusalem and is called "the crown of thorns". But, they also found pollen from about 40 other types of flowers around Jerusalem which would be reasonable according to Jewish burial customs.
At this point the only way a forger could have done this was to reenact a real crucifixion with a real person who just happens to have had the same blood type as Jesus. Even so they would have had to have been able to reproduce their own cloth that perfectly matches the cloth of the time in both weave and composition. They would have had to use Roman artifacts that were over 1,000 years old. Even if they did all that we still don't understand how the image got on the cloth, and this is after 30 years of study.
Now, even if you want to believe that there really was such a forger, that it fine, you are doing it based on the carbon dating, so it isn't as though your conclusion is baseless.
But then you are left with two very big problems to your theory that this is a forgery.
1. There are late 7th century byzantine coins which depict a shroud.
2. You have to explain the iconographic image of Christ the Pantocrator --
https://en.wikipedia.org/wiki/Christ_Pantocrator
This is the first time in history we see the iconic image of Jesus face, which we see on the Shroud, and which has been adopted since. This was made in the 6th or 7th century, almost 800 years before the supposed age of the shroud. Why this strange appearance of the face? The images of Jesus prior to this came in a wide variety, all looking relatively normal or else God like (Zeus, etc). But after this we get this very strange looking face that people even suggested Jesus might have some strange disease. However, once we did the 3d modeling we discovered that this strange looking face is what happens when you drape a cloth over a face and then flatten out the cloth. The face on the cloth of the person who was crucified was normal looking, and that is the way in which Jesus was depicted for 700 years until this one church in Jerusalem was built with this image. Now one very reasonable explanation is that this picture was based on the shroud. But if that is true then the carbon dating is wrong.
3. The image of Edessa had the face of Jesus on it, this dates to the 6th century. We don't know what this item was, but apparently it had the exact same image that the shroud has. Because this became the image for the face of Jesus from then on.
4. There is an account of the image of Jesus rising up out of a box in a big cathedral in Constantinople from around this time. There are also strange fold marks on the shroud of Turin which when replicated would explain the folds you would see if it were kept in this box and pulled up like a screen to be on display.
So yes, we do have a single piece of evidence that says it is a forgery from the 14th century but that would not explain these 4 historical accounts of a shroud or image that predate that by close to 1,000 years. It also does not explain how a forger could do such a masterful job that after 30 years scientists have not been able to figure out or recreate.
The basic premise of science is that you get "reproducible" results. You can claim that you have discovered "cold fusion" but until we can reproduce your results no one is going to accept that. This is where we are with the Shroud, no one can explain all of the questions, nor can we reproduce it.
On the other hand there is are plausible explanations for why the carbon dating says 14th century whereas the Shroud is actually much older.