Commutative affine rings

1999 ◽  
Vol 40 (1) ◽  
pp. 3-8 ◽  
Author(s):  
I. Kh. Bekker
Keyword(s):  
1972 ◽  
Vol 13 (1) ◽  
pp. 155-156 ◽  
Author(s):  
V. T. Markov
Keyword(s):  

1992 ◽  
Vol 20 (10) ◽  
pp. 2877-2902 ◽  
Author(s):  
Daniel E. Plath ◽  
Jacob Towber

1986 ◽  
Vol 98 (4) ◽  
pp. 537-537 ◽  
Author(s):  
S. Montgomery ◽  
L. W. Small
Keyword(s):  

1972 ◽  
Vol 24 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Paul Cherenack

The purposes of this paper are:(A) To show (§§ 1, 3, 5) that some of the usual notions of homotopy theory (sums, quotients, suspensions, loop functors) exist in the category of affine k-schemes where the affine rings are countably generated.(B) By example to demonstrate some of the more geometric relations between two objects of and their quotient or to study the algebraic suspension of one of them. See §§ 2.1, 2.2, 2.3, 3.(C) To prove (§4) that the algebraic suspension (in R/) of the n-sphere is homeomorphic to the n + 1 sphere for the usual topologies.(D) To show that the algebraic loop functor is right adjoint to the algebraic suspension functor (§5).These results can be viewed as a precursor of definitions for an algebraic homotopy theory from a “geometric” point of view (rather than a more algebraic standpoint employing Galois theory [5]).


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