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Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups
arxiv
,
2017.
Gavrilovich M.
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.
Publication based on the results of:
Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups
Gavrilovich M., Archive for Mathematical Logic 2018
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms. ...
Added: October 19, 2018
Gavrilovich M., / arxiv. Series arxiv "math.CT". 2017.
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of ...
Added: July 21, 2017
Balzin Edouard, / Cornell University. Series math "arxiv.org". 2014.
In the world of triangulated categories, categorical resolutions (as defined by Kuznetsov and Luntz) have been useful. One would like to have a similar notion of categorical resolution in homotopical algebra, where one works with categories which are not additive, such as the categories of E_n-algebras. Describing algebraic structures using the approach inspired by Segal, ...
Added: December 23, 2014
Prokhorov Y., / Cornell University. Series arXiv "math". 2021.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 25, 2021
Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135-168
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...
Added: September 7, 2021
Positselski L., / Cornell University. Series math "arxiv.org". 2014. No. 1404.5011.
We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to recover the abelian/exact category of modular representations of a finite group from the exact category of its l-adic ...
Added: April 22, 2014
Efimov A., / Cornell University. Series math "arxiv.org". 2013.
In this paper, we show that bounded derived categories of coherent sheaves (considered as DG categories) on separated schemes of finite type over a field of characteristic zero are homotopically finitely presented. This confirms a conjecture of Kontsevich. The proof uses categorical resolution of singularities of Kuznetsov and Lunts, which is based on the ordinary ...
Added: October 31, 2013
Positselski L., Efimov A., / Cornell University. Series math "arxiv.org". 2013. No. arXiv:1102.0261.
We define the triangulated category of relative singularities of a closed subscheme in a scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations of the related section of a line bundle, and their analogues with locally free sheaves replaced by coherent ones. The appropriate exotic derived category of coherent matrix factorizations ...
Added: December 22, 2013
Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591-612
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...
Added: September 8, 2021
Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921
In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...
Added: October 4, 2021
Positselski L., Arkhipov S., Rumynin D., Basel : Birkhauser/Springer, 2010
We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define double-sided derived functors SemiTor and SemiExt of the functors of semitensor product and semihomomorphisms, and construct an equivalence between the exotic derived categories ...
Added: March 19, 2013
Gavrilovich M., The De Morgan Gazette 2014 Vol. 5 No. 4 P. 23-32
We observe that some natural mathematical definitions are lifting properties relative to simplest counterexamples, namely the definitions of surjectivity and injectivity of maps, as well as of being connected, separation axioms T0 and T1 in topology, having dense image, induced (pullback) topology, and every real-valued function being bounded (on a connected domain). We also offer ...
Added: October 20, 2015
Rodin A., , in : Philosophy, Mathematics, Linguistics: Aspects of Interaction. : [б.и.], 2009. P. 171-175.
A perpetual change of foundations observed in the real history of the discipline is not a
historical accident but an essential feature of foundations. I distinguish between the progress of
mathematics and renewal of its foundations and show how the latter contributes to the former with
some historical examples. I also describe a mechanism of renewal of foundations, ...
Added: June 7, 2018
Shramov K., / Cornell University. Series arXiv "math". 2020.
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero. ...
Added: August 19, 2020
Shramov K., / Cornell University. Series arXiv "math". 2019.
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration. ...
Added: November 19, 2019
Positselski L., / Cornell University. Series math "arxiv.org". 2014. No. 1209.2995.
Contraherent cosheaves are globalizations of cotorsion (or similar) modules over commutative rings obtained by gluing together over a scheme. The category of contraherent cosheaves over a scheme is a Quillen exact category with exact functors of infinite product. Over a quasi-compact semi-separated scheme or a Noetherian scheme of finite Krull dimension (in a different version ...
Added: February 6, 2013
Balzin E., Успехи математических наук 2014 Т. 69 № 5(419) С. 159-160
В статье дан обзор части результатов диссертационной работы автора. Речь идет о применении идеи категорного разрешения сингулярностей, которая была активно опробована алгебраическими геометрами для триангулированных категорий, в гомотопической алгебре. В связи с тем, что возникающие тут категории не имеют никакой аддитивной структуры, возникает необходимость в разработке новых методов. В рамках формализма Сигала, который позволяет описывать ...
Added: December 24, 2014
Prokhorov Y., , in : 8th European Congress of Mathematics, Portorož, 20–26 June, 2021. : [б.и.], 2023. P. 413-437.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 13, 2023
Raikov A., Pirani M., IEEE Access 2022 Vol. 10 P. 56296-56315
The goal of the paper is to find means for the unification of human-machine duality in collective behavior of people and machines, by conciliating approaches that proceed in opposite directions. The first approach proceeds top-down from non-formalizable, cognitive, uncaused, and chaotic human consciousness towards purposeful and sustainable human-machine interaction. The second approach proceeds bottom-up from ...
Added: July 19, 2022
Athens : The Hellenic Open University, 2013
The book contains the reports of the member of the congress from the different countres. They consider the idea of the symmety in the science and in the art. ...
Added: January 30, 2014
Positselski L., / Cornell University. Series math "arxiv.org". 2012. No. 1202.2697.
We define and study the derived categories of the first kind for curved DG and A-infinity algebras complete over a pro-Artinian local ring with the curvature elements divisible by the maximal ideal of the local ring. We develop the Koszul duality theory in this setting and deduce the generalizations of the conventional results about A-infinity ...
Added: February 6, 2013
Popov V. L., Doklady Mathematics 2018 Vol. 98 No. 2 P. 413-415
The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established. ...
Added: November 13, 2018
Balzin E., Applied Categorical Structures 2017
The description of algebraic structure of n-fold loop spaces can be done either using the formalism of topological operads, or using variations of Segal’s Γ-spaces. The formalism of topological operads generalises well to different categories yielding such notions as (Formula presented.)-algebras in chain complexes, while the Γ-space approach faces difficulties. In this paper we discuss ...
Added: March 18, 2017
Busjatskaja I., Monastyrsky M. I., , in : Symmetry: Art and Science. Special Issue for the Congress-Festival of ISIS-Symmetry. : Athens : The Hellenic Open University, 2013. P. 248-253.
The paper examines the significance of Platonic Solids in different parts of modern science. ...
Added: January 30, 2014