Let A be a ring, f a nonzero divisor in A, ($) over cap A the completion of A for the (f)-adic topology. We prove that the data of a vector bundle on Spec (A) is equivalent to the data of a vector bundle on the open subset f not equal 0 of Spec (A) and on Spec (($) over cap A), together with an isomorphism of their pull back to the open subset f not equal 0 of Spec (A).
机构:
Univ Johannesburg, Dept Pure & Appl Math, ZA-2006 Auckland Pk, South AfricaNormandie Univ, GREYC, CNRS, ENSICAEN,UNICAEN, F-14000 Caen, France
Henning, Michael A.
Klavzar, Sandi
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机构:
Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia
Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
Inst Math Phys & Mech, Ljubljana, SloveniaNormandie Univ, GREYC, CNRS, ENSICAEN,UNICAEN, F-14000 Caen, France
Klavzar, Sandi
Kosmrlj, Gasper
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Inst Math Phys & Mech, Ljubljana, Slovenia
Abelium R&D, Ljubljana, SloveniaNormandie Univ, GREYC, CNRS, ENSICAEN,UNICAEN, F-14000 Caen, France
机构:
Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Peoples R China
Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R ChinaHuaqiao Univ, Sch Math Sci, Quanzhou 362021, Peoples R China