Journal of Homotopy and Related Structures最新文献_第7页

The Picard group of motivic (mathcal {A}_mathbb {C}(1)) 皮卡德集团的动机 (mathcal {A}_mathbb {C}(1))

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2018-04-20 DOI: 10.1007/s40062-018-0200-z

Bogdan Gheorghe, Daniel C. Isaksen, Nicolas Ricka

引用次数: 0

Koszul–Tate resolutions as cofibrant replacements of algebras over differential operators 微分算子上代数的协替换

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2018-03-26 DOI: 10.1007/s40062-018-0202-x

Gennaro di Brino, Damjan Pištalo, Norbert Poncin

{"title":"Koszul–Tate resolutions as cofibrant replacements of algebras over differential operators","authors":"Gennaro di Brino, Damjan Pištalo, Norbert Poncin","doi":"10.1007/s40062-018-0202-x","DOIUrl":"https://doi.org/10.1007/s40062-018-0202-x","url":null,"abstract":"Homotopical geometry over differential operators is a convenient setting for a coordinate-free investigation of nonlinear partial differential equations modulo symmetries. One of the first issues one meets in the functor of points approach to homotopical ({{{mathcal {D}}}})-geometry, is the question of a model structure on the category ({mathtt{DGAlg({{{mathcal {D}}}})}}) of differential non-negatively graded ({{{mathcal {O}}}})-quasi-coherent sheaves of commutative algebras over the sheaf ({{{mathcal {D}}}}) of differential operators of an appropriate underlying variety ((X,{{{mathcal {O}}}})). We define a cofibrantly generated model structure on ({mathtt{DGAlg({{{mathcal {D}}}})}}) via the definition of its weak equivalences and its fibrations, characterize the class of cofibrations, and build an explicit functorial ‘cofibration–trivial fibration’ factorization. We then use the latter to get a functorial model categorical Koszul–Tate resolution for ({{{mathcal {D}}}})-algebraic ‘on-shell function’ algebras (which contains the classical Koszul–Tate resolution). The paper is also the starting point for a homotopical ({{{mathcal {D}}}})-geometric Batalin–Vilkovisky formalism.","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 4","pages":"793 - 846"},"PeriodicalIF":0.5,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0202-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5012487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

The homotopy theory of operad subcategories 可操作子范畴的同伦论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2018-02-13 DOI: 10.1007/s40062-018-0198-2

Benoit Fresse, Victor Turchin, Thomas Willwacher

{"title":"The homotopy theory of operad subcategories","authors":"Benoit Fresse, Victor Turchin, Thomas Willwacher","doi":"10.1007/s40062-018-0198-2","DOIUrl":"https://doi.org/10.1007/s40062-018-0198-2","url":null,"abstract":"We study the subcategory of topological operads ({mathsf {P}}) such that ({mathsf {P}}(0) = *) (the category of unitary operads in our terminology). We use that this category inherits a model structure, like the category of all operads in topological spaces, and that the embedding functor of this subcategory of unitary operads into the category of all operads admits a left Quillen adjoint. We prove that the derived functor of this left Quillen adjoint functor induces a left inverse of the derived functor of our category embedding at the homotopy category level. We deduce from this result that the derived mapping spaces associated to our model category of unitary operads are homotopy equivalent to the standard derived operad mapping spaces, which we form in the model category of all operads in topological spaces. We prove that analogous statements hold for the subcategory of k-truncated unitary operads within the model category of all k-truncated operads, for any fixed arity bound (kge 1), where a k-truncated operad denotes an operad that is defined up to arity k.","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 4","pages":"689 - 702"},"PeriodicalIF":0.5,"publicationDate":"2018-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0198-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4534169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Mapping spaces and R-completion 映射空间和r补全

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2018-02-01 DOI: 10.1007/s40062-018-0196-4

David Blanc, Debasis Sen

引用次数: 8

A higher homotopic extension of persistent (co)homology 持久(co)同调的高同伦扩展

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-12-20 DOI: 10.1007/s40062-017-0195-x

Estanislao Herscovich

引用次数: 8

The n-fold reduced bar construction n倍减杆结构

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-10-11 DOI: 10.1007/s40062-017-0191-1

Sonja Lj. Čukić, Zoran Petrić

引用次数: 1

Homotopy of finite ringed spaces 有限环空间的同伦

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-10-07 DOI: 10.1007/s40062-017-0190-2

Fernando Sancho de Salas

引用次数: 1

Monoform objects and localization theory in abelian categories 阿贝尔范畴的单形对象与局部化理论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-09-06 DOI: 10.1007/s40062-017-0188-9

Reza Sazeedeh

引用次数: 6

Normality of algebras over commutative rings and the Teichmüller class. II. 交换环上代数的正态性及teichmller类。2

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-07-26 DOI: 10.1007/s40062-017-0174-2

Johannes Huebschmann

引用次数: 5

Normality of algebras over commutative rings and the Teichmüller class. I. 交换环上代数的正态性及teichmller类。我。

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-07-26 DOI: 10.1007/s40062-017-0173-3

Johannes Huebschmann

{"title":"Normality of algebras over commutative rings and the Teichmüller class. I.","authors":"Johannes Huebschmann","doi":"10.1007/s40062-017-0173-3","DOIUrl":"https://doi.org/10.1007/s40062-017-0173-3","url":null,"abstract":"Let S be a commutative ring and Q a group that acts on S by ring automorphisms. Given an S-algebra endowed with an outer action of Q, we study the associated Teichmüller class in the appropriate third group cohomology group. We extend the classical results to this general setting. Somewhat more specifically, let R denote the subring of S that is fixed under Q. A Q-normal\u0000S-algebra consists of a central S-algebra A and a homomorphism (sigma :Qrightarrow mathop {mathrm{Out}}nolimits (A)) into the group (mathop {mathrm{Out}}nolimits (A)) of outer automorphisms of A that lifts the action of Q on S. With respect to the abelian group (mathrm {U}(S)) of invertible elements of S, endowed with the Q-module structure coming from the Q-action on S, we associate to a Q-normal S-algebra ((A, sigma )) a crossed?2-fold extension (mathrm {e}_{(A, sigma )}) starting at (mathrm {U}(S)) and ending at Q, the Teichmüller complex of ((A, sigma )), and this complex, in turn, represents a class, the Teichmüller class of ((A, sigma )), in the third group cohomology group (mathrm {H}^3(Q,mathrm {U}(S))) of Q with coefficients in (mathrm {U}(S)). We extend some of the classical results to this general setting. Among others, we relate the Teichmüller cocycle map with the generalized Deuring embedding problem and develop a seven term exact sequence involving suitable generalized Brauer groups and the generalized Teichmüller cocycle map. We also relate the generalized Teichmüller cocycle map with a suitably defined abelian group <img> of classes of representations of Q in the Q-graded Brauer category <img> of S with respect to the given action of Q on S.","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"13 1","pages":"1 - 70"},"PeriodicalIF":0.5,"publicationDate":"2017-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0173-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5007097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3