scholarly journals Inverse limits of Macaulay's inverse systems

2019 ◽  
Vol 525 ◽  
pp. 341-358
Author(s):  
Mathias Schulze ◽  
Laura Tozzo
Keyword(s):  
Inverse Limits ◽  
Inverse Systems

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals Some categorical aspects of the inverse limits in ditopological context

2018 ◽  
Vol 19 (1) ◽  
pp. 101
Author(s):  
Filiz Yildiz
Keyword(s):  
Compatibility Condition ◽  
Natural Transformation ◽  
Inverse Limits ◽  
Infinite Products ◽  
Inverse Systems ◽  
Finite Products

<p>This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if<strong>PDitop</strong>, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category <strong>Inv<sub>ifPDitop</sub></strong> consisting of the inverse systems constructed by the objects and morphisms of if<strong>PDitop</strong>, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if<strong>PDitop</strong> and the ditopological infinite products are characterized by the finite products via inverse limits.</p>

Elementary epimorphisms

2005 ◽  
Vol 70 (2) ◽  
pp. 473-487 ◽  
Author(s):  
Philipp Rothmaler
Keyword(s):  
Inverse Limits ◽  
Elementary Chain ◽  
Flat Modules ◽  
Inverse Systems

AbstractThe concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).

Big and large continua in inverse limits of inverse systems over directed graphs

2020 ◽  
Vol 274 ◽  
pp. 107119
Author(s):  
Iztok Banič ◽  
Matevž Črepnjak ◽  
Peter Goričan ◽  
Teja Kac ◽  
Matej Merhar ◽  
...  
Keyword(s):  
Directed Graphs ◽  
Inverse Limits ◽  
Inverse Systems

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

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