{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":18,"n_cols":5,"rows_kept":18,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[5,2,5,3],[6,2,6,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[10,2,10,3],[11,2,11,3],[12,2,12,3],[16,2,16,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910827586603321"]
[null,null,"Autore",null,"Joyce Dominic D."]
[null,null,"Titolo",null,"Algebraic geometry over C[infinity]-rings / / Dominic Joyce"]
[null,null,"Pubbl/distr/stampa",null,"Providence, RI : , : American Mathematical Society, , [2019]"]
[{"$nulls":4},"©2019"]
[null,null,"ISBN",null,"1-4704-5336-3"]
[null,null,"Descrizione fisica",null,"1 online resource (152 pages) : illustrations"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 1256"]
[null,null,"Classificazione",null,"58A4014A2046E2551K10"]
[null,null,"Disciplina",null,"516.3/6"]
[null,null,"Soggetti",null,"Geometry, Algebraic"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"July 2019, volume 260, number 1256 (third of 5 numbers).\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"C[infinity]-rings -- The C[infinity]-ring C[infinity](X) of a manifold X -- C[infinity]-ringed spaces and C[infinity]-schemes -- Modules over C[infinity]-rings and C[infinity]-schemes -- C[infinity]-stacks -- Deligne-Mumford C[infinity]-stacks -- Sheaves on Deligne-Mumford C[infinity]-stacks -- Orbifold strata of C[infinity]-stacks."]
[null,null,null,"Sommario/riassunto","\"If X is a manifold then the R-algebra C[infinity](X) of smooth functions C : X [right arrow] R is a C[infinity]-ring. That is, for each smooth function f : Rn [right arrow] R there is an n-fold operation ]Phi]f : C[infinity](X)n [right arrow] C[infinity](X) acting by [Phi]f : (c1, . . . , cn) [right arrow] f(c1, . . . , cn), and these operations [Phi]f satisfy many natural identities. Thus, C[infinity](X) actually has a far richer structure than the obvious R-algebra structure. We explain the foundations of a version of algebraic geometry in which rings or algebras are replaced by C[infinity]-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C[infinity]-schemes, a category of geometric objects which generalize manifolds, and whose morphisms generalize smooth maps. We also study quasicoherent sheaves on C[infinity]-schemes, and C[infinity]-stacks, in particular Deligne- Mumford C[infinity]-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C[infinity]-rings and C[infinity]-schemes have long been part of synthetic differential geometry. But we develop them in new directions. In Joyce (2014, 2012, 2012 preprint), the author uses these tools to define d-manifolds and d-orbifolds, 'derived' versions of manifolds and orbifolds related to Spivak's 'derived manifolds' (2010)\"--"]