scholarly journals An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma

1995 ◽  
Vol 73 (3) ◽  
pp. 215-248 ◽  
Author(s):  
Jan-Hendrik Evertse
Keyword(s):  
1991 ◽  
Vol 150 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Roman Frič ◽  
Darrell C. Kent

2020 ◽  
Vol 48 (2) ◽  
pp. 211-219
Author(s):  
Daiqiang Lu ◽  
Gaoxiang Xing ◽  
Tao Luo ◽  
Qi Zhang

2020 ◽  
pp. 1-24
Author(s):  
MATTHEW WESTAWAY

Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras. In this paper, we prove that the Steinberg decomposition can be similarly deformed, allowing us to reduce representation theoretic questions about these algebras to questions about reduced enveloping algebras. We use this to derive structural results about modules over these algebras. Separately, we also show that many of the results in the preceding paper hold without an assumption of reductivity.


1975 ◽  
Vol 19 (1) ◽  
pp. 62-73 ◽  
Author(s):  
B. F. Sherman

This paper concerns the completions of partially ordered groups introduced by Fuchs (1965a) and the author (to appear); the p.o. groups under consideration are, generally, abelian tight Riesz groups, and so, throughout, the word “group” will refer to an abelian group.In section 3 we meet the cornerstone of the work, the central product theorem, by means of which we can interpret the Cauchy completion of a tight Riesz group in terms of the completion of any of its o-ideals; one particularly important case arises when the group has a minimal o-ideal. Such a minimal o-ideal is o-simple, and in section 6 the completion of an isolated o-simple tight Riesz group is shown to be a tight Riesz real vector space.


Analysis ◽  
2013 ◽  
Vol 33 (2) ◽  
pp. 189-196 ◽  
Author(s):  
Pinnangudi Narayanasubramanian Natarajan
Keyword(s):  

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