|
Books > Science & Mathematics > Mathematics > Algebra
|
Buy Now
Algebraic Geometry over $C^/infty $-Rings (Paperback)
Loot Price: R2,111
Discovery Miles 21 110
|
|
|
Algebraic Geometry over $C^/infty $-Rings (Paperback)
Series: Memoirs of the American Mathematical Society
Expected to ship within 12 - 17 working days
|
If $X$ is a manifold then the $\mathbb R$-algebra $C^\infty (X)$ of
smooth functions $c:X\rightarrow \mathbb R$ is a $C^\infty $-ring.
That is, for each smooth function $f:\mathbb R^n\rightarrow \mathbb
R$ there is an $n$-fold operation $\Phi _f:C^\infty
(X)^n\rightarrow C^\infty (X)$ acting by $\Phi _f:(c_1,\ldots
,c_n)\mapsto f(c_1,\ldots ,c_n)$, 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. The author explains the foundations of a version of
algebraic geometry in which rings or algebras are replaced by
$C^\infty $-rings. As schemes are the basic objects in algebraic
geometry, the new basic objects are $C^\infty $-schemes, a category
of geometric objects which generalize manifolds and whose morphisms
generalize smooth maps. The author also studies quasicoherent
sheaves on $C^\infty $-schemes, and $C^\infty $-stacks, in
particular Deligne-Mumford $C^\infty$-stacks, a 2-category of
geometric objects generalizing orbifolds. Many of these ideas are
not new: $C^\infty$-rings and $C^\infty $-schemes have long been
part of synthetic differential geometry. But the author develops
them in new directions. In earlier publications, the author used
these tools to define d-manifolds and d-orbifolds, ``derived''
versions of manifolds and orbifolds related to Spivak's ``derived
manifolds''.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
