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Results tagged with hyperelliptic-curves
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user 10300
3
votes
0
answers
117
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How order of divisor with support at infinity is changed at reduction?
Jing Yu in his paper "On Arithmetic Of Hyperelliptic Curves" on page 5 asserts the following
The most interesting case is certainly the case $k = \mathbb Q$ and $D \in \mathbb Z[t]$.
To decid …
- 424
7
votes
2
answers
1k
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Calculate reduction of Jacobian of hyperelliptic curve
Suppose I have a hyperelliptic curve of genus $2$ over $\mathbb Q$. I want to get information about its Jacobian reduction at prime $p$ (especially, in case $p=2$). Also I'm interesting in the group o …
- 424
4
votes
0
answers
204
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Computing Tamagawa numbers for jacobians of hyperelliptic curves
Do exist some computational approach to calculation of Tamagawa number for the jacobian of hyperelliptic curve at prime $p$?
As followed from this question one can compute $\Phi(\overline{\mathbb F}_ …
- 424
9
votes
5
answers
4k
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Good lecture notes/books on Jacobian of hyperelliptic curve
I want to understand what the Jacobian variety is from an algebraic (or arithmetic?) perspective.
I want to know:
What is the definition of the Jacobian?
Widely know facts about it.
Why the Jacobia …
- 424