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user127776
user127776
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I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisorintersection of hypersurfaces $Y$ on a smooth projective variety $X$ over a finite field, is the category of vector bundles defined on a neighborhood of the divisor$Y$ equivalent to the category of vector bundles on the formal neighborhood of the ample divisor$Y$ ($\text{dim}Y\geq 2$)? This is asking whether $\text{Leff(Y,X)}$ holds or not (This is true if we work over an algebraically closed field)

This seems to be true in the case of very ample divisors (not necessarily intersections of hypersurfacesone hypersurface). This example claims it to be true without assumptions on the field. The example does not claim the extension is unique on the neighborhood, so I am wondering whether an ample divisor $Y$ in a smooth projective variety $X$ of dimension $\geq 3$ satisfies $\text{Leff}(Y,X)$ or not? (field is not algebraically closed)

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisor on a smooth projective variety over a finite field, is the category of vector bundles defined on a neighborhood of the divisor equivalent to the category of vector bundles on the formal neighborhood of the ample divisor? (This is true if we work over an algebraically closed field)

This seems to be true in the case of ample divisors (not necessarily intersections of hypersurfaces). This example claims it to be true without assumptions on the field.

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an intersection of hypersurfaces $Y$ on a smooth projective variety $X$ over a finite field, is the category of vector bundles defined on a neighborhood of the $Y$ equivalent to the category of vector bundles on the formal neighborhood of $Y$ ($\text{dim}Y\geq 2$)? This is asking whether $\text{Leff(Y,X)}$ holds or not (This is true if we work over an algebraically closed field)

This seems to be true in the case of very ample divisors (one hypersurface). This example claims it to be true without assumptions on the field. The example does not claim the extension is unique on the neighborhood, so I am wondering whether an ample divisor $Y$ in a smooth projective variety $X$ of dimension $\geq 3$ satisfies $\text{Leff}(Y,X)$ or not? (field is not algebraically closed)

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user127776
user127776
  • 5.9k
  • 2
  • 9
  • 24

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisor on a smooth projective variety over a finite field, is the category of vector bundles defined on a neighborhood of the divisor equivalent to the category of vector bundles on the formal neighborhood of the ample divisor? (This is true if we work over an algebraically closed field)

This seems to be true in the case of ample divisors (not necessarily intersections of hypersurfaces). This example claims it to be true without assumptions on the field.

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisor on a smooth projective variety over a finite field, is the category of vector bundles defined on a neighborhood of the divisor equivalent to the category of vector bundles on the formal neighborhood of the ample divisor? (This is true if we work over an algebraically closed field)

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisor on a smooth projective variety over a finite field, is the category of vector bundles defined on a neighborhood of the divisor equivalent to the category of vector bundles on the formal neighborhood of the ample divisor? (This is true if we work over an algebraically closed field)

This seems to be true in the case of ample divisors (not necessarily intersections of hypersurfaces). This example claims it to be true without assumptions on the field.

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user127776
user127776
  • 5.9k
  • 2
  • 9
  • 24

Algebraization of vector bundles over non-algebraically closed fields

I've asked this question here but never got an answer, a simplified version of the question is the following:

Given an ample divisor on a smooth projective variety over a finite field, is the category of vector bundles defined on a neighborhood of the divisor equivalent to the category of vector bundles on the formal neighborhood of the ample divisor? (This is true if we work over an algebraically closed field)