Berkovich spaces and tubular descent

Oren Ben-Bassat; Michael Temkin

doi:10.1016/j.aim.2012.10.016

Berkovich spaces and tubular descent

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space W which we define.

Original language	English
Pages (from-to)	217-238
Number of pages	22
Journal	Advances in Mathematics
Volume	234
DOIs	https://doi.org/10.1016/j.aim.2012.10.016
State	Published - 5 Feb 2013
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referee for the detailed comments and corrections in response to the initial submission. The first author would like to thank the University of Pennsylvania and the University of Haifa for travel support, as well as Jonathan Block, Ron Donagi, David Harbater, and Tony Pantev for helpful discussions. The second author would like to thank V. Drinfeld for the invitation to visit the University of Chicago and his support, and for informing him about the correspondence with V. Berkovich. The work of M.T. was partially supported by ISF grant No. 1018/11 .

Keywords

Berkovich analytic spaces
Tubular descent

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2012.10.016

Cite this

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title = "Berkovich spaces and tubular descent",

abstract = "We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space W which we define.",

keywords = "Berkovich analytic spaces, Tubular descent",

author = "Oren Ben-Bassat and Michael Temkin",

note = "Funding Information: The authors would like to thank the anonymous referee for the detailed comments and corrections in response to the initial submission. The first author would like to thank the University of Pennsylvania and the University of Haifa for travel support, as well as Jonathan Block, Ron Donagi, David Harbater, and Tony Pantev for helpful discussions. The second author would like to thank V. Drinfeld for the invitation to visit the University of Chicago and his support, and for informing him about the correspondence with V. Berkovich. The work of M.T. was partially supported by ISF grant No. 1018/11 . ",

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AU - Temkin, Michael

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N2 - We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space W which we define.

AB - We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space W which we define.

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ER -

Berkovich spaces and tubular descent

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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