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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
0
answers
160
views
Explicit computations of Serre duality for elliptic curves
I have an elliptic curve $E$ defined over a ring $R$, I want to compute the pairing
$$
H^1(E,\mathcal{O}_E)\times H^0(E, \Omega_E^1){\rightarrow}R.
$$
Clearly we have that $H^0(E, \Omega_E^1)=R \langl …
3
votes
What does "trait" mean?
Someone means something as $\text{Spec}(k[[x]])$: his spec is $0$ and $(x)$, so it is an enlargement of the point $(0)$ of $\text{Spec}(k)$, for this reason it could be named as a "trait". It is insid …