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Algebraic geometry over $C^\infty$-rings

Abstract:

If $X$ is a smooth manifold then the $\mathbb R$-algebra $C^\infty(X)$ of smooth functions $c:X\to\mathbb R$ is a $C^\infty$-$ring$. That is, for each smooth function $f:{\mathbb R}^n\to\mathbb R$ there is an $n$-fold operation $\Phi_f:C^\infty(X)^n\to C^\infty(X)$ acting by $\Phi_f:(c_1,\ldots,c_n)\mapsto f(c_1,...,c_n)$, and these operations $\Phi_f$ satisfy many natural identities. Thus, $C^\infty(X)$ actually has a far richer structure than the obvious $\mathbb R$-algebra structure. We ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/H035303/1
EP/J016950/1
Publisher:
American Mathematical Society
Journal:
Memoirs of the American Mathematical Society More from this journal
Volume:
60
Issue:
1256
Publication date:
2019-09-06
Acceptance date:
2016-10-31
EISSN:
1947-6221
ISSN:
0065-9266
ISBN:
9781470436452
Keywords:
Pubs id:
pubs:195876
UUID:
uuid:aa0cbb5c-59b9-4649-ae37-ce630c89dfe3
Local pid:
pubs:195876
Source identifiers:
195876
Deposit date:
2016-11-01

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