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.
Bibliographical noteFunding 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 .
- Berkovich analytic spaces
- Tubular descent
ASJC Scopus subject areas
- Mathematics (all)