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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 …
marco's user avatar
  • 109
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 …
marco's user avatar
  • 109