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1. |
Record Nr. |
UNINA9910131233803321 |
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Autore |
Rocher Guy |
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Titolo |
La crise des valeurs au Québec / / Guy Rocher |
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Pubbl/distr/stampa |
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Chicoutimi : , : J.-M. Tremblay, , 2007 |
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ISBN |
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Descrizione fisica |
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1 online resource (12 pages) |
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Collana |
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Classiques des sciences sociales |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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2. |
Record Nr. |
UNINA9910827586603321 |
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Autore |
Joyce Dominic D. |
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Titolo |
Algebraic geometry over C[infinity]-rings / / Dominic Joyce |
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Pubbl/distr/stampa |
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Providence, RI : , : American Mathematical Society, , [2019] |
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©2019 |
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ISBN |
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Descrizione fisica |
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1 online resource (152 pages) : illustrations |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 1256 |
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Classificazione |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"July 2019, volume 260, number 1256 (third of 5 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 -- |
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Deligne-Mumford C[infinity]-stacks -- Sheaves on Deligne-Mumford C[infinity]-stacks -- Orbifold strata of C[infinity]-stacks. |
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Sommario/riassunto |
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"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)"-- |
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