who wrote John 21 and John 1-20?

I think that John 21 was not written by the same person that wrote John 1-20.

I find the following reasons:

1. Chapter 20 ends in vv. 30-31 with a fully-fledged conclusion, that points back to the σημεῖα (signs), that can be found in John 2-12. Therefore, unless the contrary is proved, I understand John 20,30-31 as the conclusion of John 1-20 (whether you include the Prologue or not).

2. John 21,24 says the the beloved disciple wrote ταῦτα. It is reasonable to think that ταῦτα refers to what comes before, that is to the Gospel as a whole down to the first conclusion in John 20,30-31.

3. I find six reasons to think that Chapter 21 is not written by the beloved disciple who wrote John 1-20. I list them as follows:

3.1. John 21,24 says that "we know that his witness is true" (οἴδαμεν ὅτι ἀληθὴς αὐτοῦ ἡ μαρτυρία ἐστίν). The verb is in first plural, so that whoever is speaking can be easily distinguished from the beloved disciple, that is referred to in third person: "he".

3.2. If the person speaking were the same as the author of John 1-20, he would be a person who testifies on his own behalf. As John 5,31 says: "If I testify on my own behalf, my testimony cannot be verified" (Ἐὰν ἐγὼ μαρτυρῶ περὶ ἐμαυτοῦ, ἡ μαρτυρία μου οὐκ ἔστιν ἀληθής).

3.3. John 21,20-23 says that Jesus didn't say that the beloved disciple wouldn't die, contrary to the word spread among the brothers. These verses make sense if they were written after the death of the beloved disciple: the author seems worried that some brothers might think that Jesus was wrong. Therefore the beloved disciple didn't wrote these verses.

3.4. The fact that we find a conclusion in John 20,30-31 make it plausible the once the Gospel ended there, and chapter 21 was added subesequently. The fact that the conclusion in 20,30-31 is not modified when chapter 21 is added leads to think that the author of John 21 didn't think he could change what was already written. This doens't happen in John 1-20, whenever the
test is modified. For instance, in chapter 4,2 a correction is inserted within the text. The author of John 21 doesn't take the same liberty.

3.5. Chapter 21 names some disciples that are never named before: that is, the sons of Zebedee. It is striking that they are never named in John 1-20. Whatever the reason, it no longer stands when John 21 was written.

3.6. Chapter 21 uses 174 different words. 27 of them are not existent in John 1-20. For instance, in chapter 6 fish is ὀψάριον, while ἰχθύς is never used. Chapter 21 uses ἰχθύς. It is unlikely that the author of John 21 is the same as the author of John 1-20.

I think that 3.1-2 are the strongest reasons, that give me certainty. I recognise that the following reasons do not provide full evidence. If considered separately, they make it more likely that the author is different. All together, they make a strong case against identity of author.