Similarly, we have $$ h(\mathbb{P}^n) \; \cong \; h(1) \; \oplus \; \mathbb{L} \; \oplus \; \mathbb{L}^{\otimes 2} \; \oplus \; \cdots \; \oplus \; \mathbb{L}^{\otimes n} $$ and this corresponds to the formula we saw for the number of points of \(\mathbb{P}^n\) over \(\mathbb{F}_q\): $$ 1 \; + \; q \; + \; \cdots \; + \; q^n $$ But curves and other varieties typically decompose into motives
that are not just tensor powers of the Lefshetz motive \(\mathbb{L}\).

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