I've just read the proof of $\S4$ (iv) in Mumford's "Abelian Varieties", on page 42-43, which says that multiplication by $n$ not divisible by $p=\text{char}(k)$ on an abelian variety $X$ is surjective.  I can understand that it works (as in, I can follow the proof line by line), yet I don't have intuition for it. In particular, I don't understand why does passing to tangent spaces work. It may be my poor understanding of tangent spaces and differentials.  It seems to say something along the lines of "surjectivity of multiplication by $n$" can be checked on first order linear approximations". Does this make any sense? Would this make sense for more general isogenies? A reference where this is discussed in more detail would also be welcome.
According with Mumford the answer is yes, but there are some obscure points in the proof.  We know that there exists a very ample line bundle on $A$ since every abelian variety is projective. Hence, via some corollaries of the Theorem of the Cube, we get an ample line bundle whose restriction to the kernel of $n_A$ is both the trivial bundle and very ample. This should imply that the dimension of $\ker n_A$ is $0$.  Furthermore, Mumford says that the fact that the dimension of the kernel is $0$ implies the surjectivity of $n_A$.  Is anybody able to clarify these two points to me?  Thanks in advance!
Partial adb restore ICS devices support creating backups using adb backup, and restoring them using adb restore. Using adb backup, one can select that everything should be backed up, or only a certain package.  However, adb restore lacks all the options of adb backup. When I call adb restore backup.ab, where backup.ab is only the backup of a single package, the phone shows me a warning dialog saying that all settings are going to be lost after restoring the backup. Is it true that restoring a single package backup wipes all data on the phone? If yes, is it somehow possible to restore a single package using adb restore? Why with two classes, LDA gives only one dimension? If I enter the US by land, not needing ESTA, would I then need ESTA to enter by air 3 days later? I am a UK citizen, and therefore qualify for the USA's  (VWP). If I enter by  I need to apply for (and pay for) ESTA beforehand. If I enter by , I don't need ESTA. 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