| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910697497603321 |
|
|
Autore |
Headd Brian |
|
|
Titolo |
Do business definition decisions distort small business research results? [[electronic resource] ] : an Office of Advocacy working paper / / Brian Headd and Radwan Saade |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
[Washington, D.C.] : , : SBA Office of Advocacy, , [2008] |
|
|
|
|
|
|
|
Descrizione fisica |
|
2 unnumbered pages : digital, PDF file |
|
|
|
|
|
|
Collana |
|
Small business research summary ; ; no. 330 |
|
|
|
|
|
|
Altri autori (Persone) |
|
|
|
|
|
|
Soggetti |
|
Business enterprises - United States |
Small business - United States - Growth |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Title from title screen (viewed on Aug. 20, 2008). |
"August 2008." |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2. |
Record Nr. |
UNINA9910793890203321 |
|
|
Autore |
Joyce Dominic D. |
|
|
Titolo |
Algebraic geometry over C[infinity]-rings / / Dominic Joyce |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Providence, RI : , : American Mathematical Society, , [2019] |
|
©2019 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (152 pages) : illustrations |
|
|
|
|
|
|
Collana |
|
Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 1256 |
|
|
|
|
|
|
|
|
Classificazione |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
"July 2019, volume 260, number 1256 (third of 5 numbers)." |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
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)"-- |
|
|
|
|
|
| |