Exercise 110.49.8. On a separated scheme $X$ of finite type over a field: Give an example of a Cartier divisor which is not the difference of two effective Cartier divisors. Hint: Find some $X$ which does not have any nonempty effective Cartier divisors for example the scheme constructed in [III Exercise 5.9, H]. There is even an example with $X$ a variety – namely the variety of Exercise 110.49.9.
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