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Let's say I have two abelian varieties, $A$ and $B$, and I take their coproduct. My intuition says that $\dim(A+B) = \dim(A) + \dim(B)$. Is this accurate?

mwt
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gradintherockies
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    Which category are you working in? In the category of schemes/algebraic varieties, coproduct is disjoint union. In the category abelian varieties, it is the fibered product. – Aphelli Jun 14 '20 at 21:46

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