Exercise 111.44.3 (0DB6)—The Stacks project

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Table of contents
Part 9: Miscellany
Chapter 111: Exercises
Section 111.44: Cohomology revisited
Exercise 111.44.3 (cite)

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Exercise 111.44.3. Let $X$ be a projective surface over an algebraically closed field $k$ . Prove there exists a proper closed subscheme $Z \subset X$ such that $H^1(Z, \mathcal{O}_ Z)$ is nonzero. Hint: Use Exercise 111.44.2.

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