scholarly journals The homological dimension of commutative group schemes over a perfect field

1970 ◽  
Vol 16 (3) ◽  
pp. 436-441 ◽  
Author(s):  
J.S Milne
Keyword(s):  
Commutative Group ◽  
Homological Dimension ◽  
Perfect Field ◽  
Group Schemes

scholarly journals Polylogarithm for families of commutative group schemes

2018 ◽  
Vol 27 (3) ◽  
pp. 449-495 ◽  
Author(s):  
Annette Huber ◽  
Guido Kings
Keyword(s):  
Commutative Group ◽  
Group Schemes

scholarly journals Commutative group algebras and Prufer groups

2010 ◽  
Vol 41 (1) ◽  
pp. 85-95
Author(s):  
P. V. Danchev
Keyword(s):  
Group Ring ◽  
Quotient Group ◽  
Commutative Group ◽  
Group Algebras ◽  
Direct Factor ◽  
Perfect Field ◽  
Characteristic P ◽  
Arbitrary Characteristic ◽  
Direct Sum ◽  
Normalized Units

Suppose $G$ is a multiplicatively written abelian $p$-group, where $p$ is a prime, and $F$ is a field of arbitrary characteristic. The main results in this paper are that none of the Sylow $p$-group of all normalized units $S(FG)$ in the group ring $FG$ and its quotient group $S(FG)/G$ cannot be Prufer groups. This contrasts a classical conjecture for which $S(FG)/G$ is a direct factor of a direct sum of generalized Prufer groups whenever $F$ is a perfect field of characteristic $p$.

The higher-dimensional Contou-Carrère symbol and commutative group schemes

2020 ◽  
Vol 75 (3) ◽  
pp. 572-574 ◽  
Author(s):  
S. O. Gorchinskiy ◽  
D. V. Osipov
Keyword(s):  
Commutative Group ◽  
Group Schemes ◽  
Higher Dimensional

scholarly journals Deformations and liftings of finite, commutative group schemes

1968 ◽  
Vol 5 (4) ◽  
pp. 317-334 ◽  
Author(s):  
Frans Oort ◽  
David Mumford
Keyword(s):  
Commutative Group ◽  
Group Schemes

scholarly journals COMPARISON OF KUMMER LOGARITHMIC TOPOLOGIES WITH CLASSICAL TOPOLOGIES

2021 ◽  
pp. 1-31
Author(s):  
Heer Zhao
Keyword(s):  
Multiplicative Group ◽  
Commutative Group ◽  
Group Schemes ◽  
Algebraic Tori ◽  
Etale Cohomology ◽  
Special Cases ◽  
Étale Cohomology ◽  
Log Scheme

Abstract We compare the Kummer flat (resp., Kummer étale) cohomology with the flat (resp., étale) cohomology with coefficients in smooth commutative group schemes, finite flat group schemes, and Kato’s logarithmic multiplicative group. We are particularly interested in the case of algebraic tori in the Kummer flat topology. We also make some computations for certain special cases of the base log scheme.

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