I have an urge to engage in Korean nationalists claims internet memes, but you can read about some of the development of the Katana on our FAQs. In short: no. It was developed due to warfare conditions in Japan.
On the topic of korean vs japanese, this is not a question with a binary answer. One of the biggest hurdles on whether something is “korean” or “japanese” in early japan is that there’s was a deep and critical influence on the formation of “japan” that came from the korean peninsula. This includes swordmaking and metallurgy.
Let me illustrate this issue by rephrasing the question two different ways:
“Did the katana come from korea fully formed?” The answer would be no, japan developed its own tradition independent of the korean peninsula.
“Did the katana originate only from indigenous japanese invention?” The answer again would be no, swordmaking and metallurgy has clear origins from the korean peninsula.
Neither extreme is correct, even though some will tend towards whichever extreme glorifies “their side” the most. This is where “korean” and “japanese” as modern constructs get in the way because unfortunately history is not always about the past but it’s also about what present people want to be the case.
I mentioned that there was a deep influence on metalworking and swordmaking in japan that came from the korean peninsula:
In the fifth century, perhaps beginning between A.D. 425 and 450, the quantity of iron from sites of all types in Japan grew dramatically. For example, at Nonaka Tomb, a mere satellite of the giant 225-metre-long, moated Hakayama Tomb in Osaka, archaeologists have uncovered ten suits of iron armour complete with helmets buried in a wooden box; another receptacle hid one more suit. In addition, the deceased had interred 169 iron swords, three iron spear points, and about 300 arrowheads. At Ariyama Tomb of the same era (also in Osaka), scientists found [many weapons]
What is more, the source of almost all this iron must have been continental, and most likely Korea, not iron-poor Japan. Recently archaeologists have discovered Enjo site north of Kyoto, where craftsmen smelted into tools and ingots iron sand collected from the bottoms of japanese rivers. At present [1996], Enjo is considered the oldest iron-smelting site in Japan, but it dates from no earlier than the late fifth century. The clear implication is that nearly all the iron to make the first Japanese weapons and tools – from the primitive iron shoes of the late Yayoi period to the suits of fifth century armor – came from Korea.
Other archaeological evidence also supports the view that inhabitants of the archipelago developed their iron-working capabilities with the aid of peninsular techniques during the early and mid-fifth century. Along with armor, spear points, and blades for hoes and spades, tools that smiths used to forge other iron implements commonly appear in japanese tombs of the mid fifth century. Implements of the smithy trade, such as large pliers, mallets, chisels, and anvils, turn up in japanese tombs, and they are identical to examples found in southern Korea, especially in Shilla and Kaya. These tools suggest that the residents of the archipelago followed the southern korean tradition of bloomery technology; indeed, later japanese furnaces (tatara) seem to have been a variant of the bloomery. Ancient japanese thus preferred the southern korean version of the iron-working to the chinese.
Not only that, but it seems that the smiths themselves are more than likely to have been of korean origin, which might be obvious if you think about how late iron smelting happened in japan.
A number of impressive linguistic and orthographic indicators of korean origing or influence have already been identified in the text of the inscription [on the Inariyama Tumulus Sword, dating from A.D. 471]. As studies proceed, there is little question but that still more evidence of a continental origin for, or at the very least strong continental influence operating upon, the author or authors of this text.
Another factor to be taken into account is that there are forms of swords in korea, the hwando, that share visual similarities to japanese katana, i.e. single edge, slight curve. Tthat often leads to confusion but I’ve not seen any evidence that their similarities stem from either side actively taking inspiration from the other rather than because they share a common tradition and similar purpose.
I tend to often see the opposite being stated incorrectly, i.e. that korean hwando were based on the katana. Unfortunately korean history is very poorly understood in the west and japanese history & imagery is better known so people are misled by cosmetic similarities. Because of things like this koreans, especially korean academics, are often more interested in pointing out the differences between hwando and katana than in claiming that the katana is korean.
I’m not sure exactly what you were told, but from the way its written I get the impression that they would’ve been referring to the korean roots. But I would suggest that neither is the case, korean hwando aren’t based on katanas and neither are katanas based on hwando, regardless of a common root.
EDIT: The thread had to be temporarily locked due to the aggressive nature that the responses took so I won't continue that conversation and clarify some things here instead to avoid it being locked again.
I would suggest that swords (or generally any other invention) don't come out of the ether whole and complete. They are the result of mineralogical and metallurgical processes, their designs are often the result of adjustments to already existing patterns.
Japan is relatively unique in that it took processes from southern Korea as a whole entity rather than through a process of absorption over time. This was most likely through mass population transfer, regardless of whether one subscribes to the conquest or the immigration theory, of skilled craftsmen. That doesn't mean that it retained a wholly korean model until the invention of the 15th century, but it does mean that there's a common base that must be acknowledged in answering the question of "how did the katana come about". It didn't spring out of nowhere.
It's also something that must be noted in answering the OPs request to address the specific aspect of korean influence on the katana. It's important to understand where the question came from and why it was asked. As such we must explicitly note where and how korean influence applies to japanese sword making. And I would suggest that "Korean nationalists claims internet memes" is not an appropriate answer to the question OP posed.
I realize that the katana has a special place in the japanese identity, which probably explains why the responses were aggressive. Another aspect that plays into it is that it's been a persistent issue in Japan that korean influence in particular must be minimized and trivialized when addressing the roots of japanese culture.
The following extract speaking about the japanese press' reporting of the Inariyama sword find is illustrative:
Press accounts concerning this important find are ranking [the excavation of the epitaph from the grave of O Yasumaro], together with the Takamatsuzuka murals and the Inariyama tumulus sword inscription, as one of the "Three Great Postwar Finds" of japanese archeology and prehistory. Unfortunately, these same press accounts are also stressing the sensational aspects of the discovery, and are making unsupported claims concerning the connection of this find with the question of the authenticity of the received text of the Kojiki. But what none of the japanese newspaper notices of this discovery have yet reported to their readers is that the chinese language of the inscription contains a startling linguistic koreanism, [details on the use of zhi]. Such employment of the word zhi would be totally ungrammatical for chinese, but it is usage that is remarkably well attested from early epigraphical specimens of chinese as it was written in Korea from the sixth through the mid-eighth centuries. It will be interesting to see how long the japanese reading public is kept in the dark concerning this startling koreanism in the Yasumaro epitaph.
I would repeat what I said elsewhere. History should be about history, not about what present peoples would like history to be.
I'll point out to anyone who has attachment to the katana that pointing out it stems from a root of technology and craftsmanship sourced from southern Korea does not in any way invalidate whatever attachment one might take from its properties. If one is using it as a vehicle for self-identify then I would urge a consideration of why an object is so important to that identity.
First thing first, some clarifications are needed concerning the term "katana."
The general term for traditional Japanese sword is nihonto (日本刀), and this is the preferred term used by experts of the subject. In our everyday conversation, many people (in both Japan and abroad) use katana as a very loose catch-all label for many different styles of nihonto that feature the iconic long, narrow and slightly curved single-edge blade. This is somewhat comparable to referring to all types of short-barrelled firearms as simply “Glocks.” There are many different styles of nihonto emerged throughout its 1500+ years of evolution on the Japanese archipelago, many of them feature that iconic curved blade (e.g. tachi, oodachi, nagamaki and many more), and others do not (such as chokuto types and the rather unusual shichishito.) Scholars of nihonto generally use katana to refer to a narrow subcategory of Japanese swords – uchigatana (打刀) – a particular bladeform and corresponding koshirae or mounting style that first emerged during the Nanboku-cho period (1336 - 1392), and fully matured and became widely popular around the late Muromachi period (c. mid to late 16th century).
It is also important to be mindful that lines dividing different “categories” of curved Japanese swords are not static and clear cut. While one could easily see clear differences of blade design between a 8th century Heian period tachi and a 16th century Muromachi era uchigatana – for the former tend to have longer cutting edge (~75cm-90cm), much narrower blade haba (width) and always comes with suguha (straight crystallization line pattern along the cutting edge), whereas the latter tend to have shorter blade length (~65cm -75cm), wider haba, and much greater variety of hamon style – the same CANNOT be said when comparing a tachi and a uchigatana blade both made in the late Edo period. The distinctions in terms of blade shape and construction b/w tachi and uchigatana swords have eroded throughout Edo period, and in many cases later tachi and uchigatana blades are indistinguishable except in mei (inscriptions on nakago) orientation and koshirae style.
Sources and further readings (sorry in Japanese):
伊藤 三平 『江戸の日本刀―新刀、新々刀の歴史的背景』（２０１６） ISBN-10: 488594502X
永山 光幹『刀剣鑑定読本』(1979)
本阿弥光遜 『日本刀の掟と特徴』(1999) ISBN-10: 493824151X
