Exercise 111.26.6 (02E4)—The Stacks project

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Part 9: Miscellany
Chapter 111: Exercises
Section 111.26: Hilbert functions
Exercise 111.26.6 (cite)

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Exercise 111.26.6. Let $A = k[x, y]/(xy)$ with $k$ algebraically closed. What are all possible Euler-Poincaré functions on finite $A$ -modules in this case?

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