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Results tagged with ag.algebraic-geometry
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user 21
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
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1
answer
105
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Is the total space of a module connected?
Let $A$ be a ring and $E$ a module. If $\mathrm{spec} A$ is connected, then so is $\mathrm{spec} S^\bullet E$. If this is not true in general, then what are some minimal conditions that make it true?
- 313
1
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How duality follows from a six functor formalism
@MarcHoyois It would help to have a further comparison between $\mathrm{hom}(1_S, f_!f^!M[m])$ and a naive definition of homology such as $H^{m}(X, M)^\lor$ in the case of field coefficients.
- 313
4
votes
If $\Omega_{X/Y}$ is locally free of rank $\mathrm{dim}\left(X\right)-\mathrm{dim}\left(Y\ri...
Let X = spec A be an affine integral scheme of dimension one which is not smooth. Smoothness may be checked smooth-locally on the source (given U --> V if there exists a W --> U which is smooth and su …
- 313
15
votes
1
answer
764
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Crystalline realization of mixed Tate motives
Deligne and Goncharov, in their article of 2005, mention that the crystalline realization functor has yet to be worked out. What's the current state of the literature on this? And how big of an issue …
- 313