I am curious about a bit of academic pedantry of trivial importance.

If I wanted to put kanji in 日本人ではありません, would I use 有りません? This looks weird to
me because 有 has some connotations of possession as opposed to 居る, for
example.
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2013-01-31T01:45:54.170
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2014-04-05T05:02:35.870
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question
kanji
kanji 有る, usage in the negative be verb
There are two kanji for verb ある that are commonly used: 有る and 在る. But neither
is natural in your sentence: 日本人では有りません and 日本人では在りません.

Note that this is not because of the negation. 日本人で有る and 日本人で在る also look
weird.

In modern Japanese, words with little semantic value are usually written in
hiragana. ある in 日本人である is used as a copula in combination with で. Although ある
is a verb, it works almost as a function word in these sentences, and
therefore it is usually written in hiragana.

Here are some other examples:

> 本を机の上に **置く** 。  
>  雨が降る前に買い物に行って **おく** 。
>
> 急いては **事** を仕損じる。  
>  車を運転する **こと** ができる。
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2013-01-31T02:09:09.433
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If you were determined to write it in Kanji では在りません would be the correct
choice in your example. However, as @Tsuyoshi_Ito points out, it's not natural
and is generally not written in Kanji.
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2014-04-04T06:30:46.637
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ではありません in your example sentence is a form of copula (である) and as such it is
written using hiragana in modern Japanese. Words that are used in auxiliary
way in the structure of the sentence are pretty much always written only using
hiragana.

There's also quite a lot of other words, including verbs, that are normally
written using hiragana. "To be" verbs ある and いる belong to this category.

* * *

In addition to great explanation in Tsuyoshi Ito's answer, please also note
that ない, the negative form of ある, is sometimes written using a different
kanji: 無い. This kanji has a meaning of non-existence. I understand it's used
rather in set phrases than commonly for all situations. There are
words/expressions which combine both kanji for positive (有) and negative (無)
aspect of ある, for example:

  * 有{あ}ること無{な}いこと - mixture of facts and fiction 
  * 有{あ}るか無{な}きか - so slight as to be all but non-existent
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answer