Lefschetz fixed point theorem in terms of cohomology

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In the some books and webpages for the definition of lefschetz fixed point writer use $ \mathbb{Q}$ as a coefficient

(https://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem) and some writer use $ \mathbb{Z}$.

Does it make any differences to use different modules ? In addition, if we use $\mathbb{Q}$ it is easy to formulate lefschetz fixed point in terms of cohomology by using universal coefficient theorem but is it easy when we use $ \mathbb{Z}$ ?