I am interested in learning about super algebraic geometry (some objects I am studying seem to be naturally superstacks, at least in some sense). What would be the best reference for the subject? I am particularly interested in (quasi)coherent sheaves over superschemes and on criteria for when a global section is $\otimes$-nilpotent (that is $s^{\otimes n}=0$ for some n).


EDIT: I am intersted mainly in places where the theory is developed integrally, so you can have elements in odd degree whose square is 2-torsion but not 0.



Quasicoherent sheaves on superschemes
Some basic references are:


1. the book by Manin Gauge Field Theory and Complex Geometry ;
2. the first paper by Delinge in Quantum Fields and Strings: A Course for Mathematicians ;
3. the recent paper on the Arxiv by Donagi and Witten Supermoduli Space Is Not Projected .


About your question, my guess would be the following. Let $X$ be a super-scheme and $X^{red}$ the reduced space. There is a natural the embedding 
$$\iota\colon X^{red} \to X$$
then $s$ is nilpotent if and only if $\iota^\* s=0$, or it is nilpotent.


(I might have been naif on your definition of $\otimes$-nilpotent)


An easy example. Consider the affine line $\mathbb{A}^{0|1}$. Take the odd function $\eta$, then $\eta\otimes\eta=\eta^2(1\otimes 1)=0$ but $\eta$ is not. In this case, $X^{red}$ is a point and $\iota^\*\eta=0$. (The sheaf I am considering is just the structure sheaf.) 


In general, if $\iota^\*s=0$, then, locally, all terms of $s$ will have non-trivial odd factors; so $s^{\otimes n}=0$ for $n$ big enough.


