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oleout
  • Member for 3 years, 11 months
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A non-ordinary singularity "splitting" into another non-ordinary singularity on a curve
@Sasha I believe an ordinary singular point $P$ of multiplicity $m$ would have $m$ distinct tangents passing through it. Otherwise, then we would have tangent of higher multiplicities.
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A non-ordinary singularity "splitting" into another non-ordinary singularity on a curve
@Sasha Did the non-ordinary point really end up becoming another non-ordinary point, or were there mistakes in my steps? If it's the former, how can I compute the genus of the curve?
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Character group functor of an exact sequence of algebraic groups
Okay thank you. I've found the reference, this is Theorem 6 of Chapter VII.3 of Serre's Algebraic group and class fields.
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Is there a Rosenlicht's lemma for semi-abelian varieties?
Thanks for the reference, it was very clear.
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The $H^1$ of a smooth curve and its (generalized) Jacobian variety
@LaurentMoret-Bailly Thank you, I've never thought of it before. I've edited the question, this was what I really wanted to know.
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The $H^1$ of a smooth curve and its (generalized) Jacobian variety
@abx My bad, I should've assumed that $C$ does not have genus zero, because otherwise the Jacobian is trivial here.
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The $H^1$ of a smooth curve and its (generalized) Jacobian variety
@LaurentMoret-Bailly I know $\mathrm{Pic}(\bar{X})$ can be defined, but what is the issue when considering only degree 0 divisor classes to define $\mathrm{Pic}^0(\bar{X})$? Did I misunderstand something?
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