I see this term in a paper. There is no abelian variety whatsoever involved. There is an original category which consists of $Z\_p$ modules with some properties, lets denote as $\mathfrak{C}$, then the author says that $\mathfrak{C}\otimes Q\_p$ is its "isogeny category". What is this supposed to mean? Is it some "change of base"? Or are there general notion of "isogeny category"?
Thank you.



what is isogeny category?
As Pete Clark intimates in his comment: If you have a category $\mathfrak C$ in which the Hom sets are $R$-modules, and composition is $R$-bilinear, and if $S$ is an
$R$-algebra, then you can form the category $\mathfrak C \otimes\_R S$ in which you tensor all Hom sets by $S$ over $R$. 


If $\mathfrak C$ is the category of abelian varieties, then taking $R = \mathbb Z$ and
$S = \mathbb Q$, this construction leads to the category of abelian varieties "up to isogeny", or "isogeny category" of abelian varieties, hence the name in general.


