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Better spelling "DeRham", not derham... I can't figure out how to change this... moderators? The cohomology of the complex of differential forms on a smooth manifold with differential given by exterior derivative.

5 votes
0 answers
142 views

algebraic de Rham cohomology of toric varieties (reference request)

I haven't been able to find anything workable yet, but I'm looking for a reference on the de Rham cohomology of toric varieties, where as many as possible of the following conditions are handled: Pos …
Somatic Custard's user avatar
2 votes
1 answer
291 views

Where does this clever choice of differential come from? (calculating $\mathrm{H}^1_{\mathrm...

In these notes of Kedlaya, he calculates the de Rham cohomology of an affine part $X$ of an elliptic curve $E$ over a field $K$, given by $y^2 = P(x) = x^3 + ax + b$. He uses these relations: $0 = y^ …
Somatic Custard's user avatar
2 votes
0 answers
175 views

vanishing of higher algebraic de Rham cohomology and sheaves of differentials for singular c...

I'm looking for some results or references about de Rham cohomology of curves in less-than-optimal cases. The two vanishing results I care about are: $H^{k}_{\text{dR}}(X) = 0$ for $k>2$, since $H^{ …
Somatic Custard's user avatar