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3
votes
Accepted
Extending descent data from the special fiber of an extension of DVR's
This seems to be a gap in the proof mentioned above, since Lemma D.1 in its present formulation does not seem to imply that $\varphi$ is a descent datum as claimed (i.e., that it satisfies the cocycle …
1
vote
Pathological behavior of Lie algebra under a map of abelian schemes
If I am not mistaken, the claim that $\mathrm{Lie}(u')$ is not an inclusion of a direct summand is erroneous. Here is why.
Let $G'$ be the abelian $R'$-scheme with generic fiber $F'_K/E'_K$. Then acc …
2
votes
Jacobian of a semistable curve
One may consult Corollary 12.5 in Oda, Seshadri "Compactifications of the generalized Jacobian variety" for a seemingly more complete argument.