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Non-Elliptic Webs and Convex Sets in the Affine Building 仿射结构中的非椭圆腹板和凸集
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-04-28 DOI: 10.4171/dm/802
Tair Akhmejanov
{"title":"Non-Elliptic Webs and Convex Sets in the Affine Building","authors":"Tair Akhmejanov","doi":"10.4171/dm/802","DOIUrl":"https://doi.org/10.4171/dm/802","url":null,"abstract":"We describe the $mathfrak sl_3$ non-elliptic webs in terms of convex sets in the affine building. Kuperberg defined the non-elliptic web basis in work on rank-$2$ spider categories. Fontaine, Kamnitzer, Kuperberg showed that the $mathfrak sl_3$ non-elliptic webs are dual to CAT(0) diskoids in the affine building. We show that each such dual diskoid is the intersection of the min-convex and max-convex hulls of a generic polygon in the building. Choosing a generic polygon from each of the components of the Satake fiber produces the duals of the non-elliptic web basis. The convex hulls in the affine building were first introduced by Faltings and are related to tropical convexity, as discussed in work by Joswig, Sturmfels, Yu and by Zhang.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"393 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76674219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
The universal de Rham / Spencer double complex on a supermanifold 超流形上的通用德·拉姆/斯宾塞双复合体
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-04-22 DOI: 10.25537/dm.2022v27.489-518
S. Cacciatori, S. Noja, R. Re
{"title":"The universal de Rham / Spencer double complex on a supermanifold","authors":"S. Cacciatori, S. Noja, R. Re","doi":"10.25537/dm.2022v27.489-518","DOIUrl":"https://doi.org/10.25537/dm.2022v27.489-518","url":null,"abstract":"The universal Spencer and de Rham complexes of sheaves over a smooth or analytical manifold are well known to play a basic role in the theory of D-modules. In this article we consider a double complex of sheaves generalizing both complexes for an arbitrary supermanifold, and we use it to unify the notions of differential and integral forms on real, complex and algebraic supermanifolds. The associated spectral sequences give the de Rham complex of differential forms and the complex of integral forms at page one. For real and complex supermanifolds both spectral sequences converge at page two to the locally constant sheaf. We use this fact to show that the cohomology of differential forms is isomorphic to the cohomology of integral forms, and they both compute the de Rham cohomology of the reduced manifold. Furthermore, we show that, in contrast with the case of ordinary complex manifolds, the Hodge-to-de Rham (or Frölicher) spectral sequence of supermanifolds with Kähler reduced manifold does not converge in general at page one.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"116 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79456818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
On Unramified Brauer Groups of Torsors over Tori 托利上托利的未分枝Brauer群
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-04-19 DOI: 10.4171/dm/776
E. Bayer-Fluckiger, R. Parimala
{"title":"On Unramified Brauer Groups of Torsors over Tori","authors":"E. Bayer-Fluckiger, R. Parimala","doi":"10.4171/dm/776","DOIUrl":"https://doi.org/10.4171/dm/776","url":null,"abstract":"In this paper we introduce a method to obtain algebraic information using arithmetic one in the study of tori and their principal homogeneous spaces. In particular, using some results of the authors with Tingyu Lee, we determine the unramified Brauer groups of some norm one tori, and their torsors.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"44 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82433921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
On the relationship between logarithmic TAQ and logarithmic THH 对数TAQ与对数THH的关系
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-04-07 DOI: 10.4171/dm/839
T. Lundemo
{"title":"On the relationship between logarithmic TAQ and logarithmic THH","authors":"T. Lundemo","doi":"10.4171/dm/839","DOIUrl":"https://doi.org/10.4171/dm/839","url":null,"abstract":"We provide a new description of logarithmic topological Andre-Quillen homology in terms of the indecomposables of an augmented ring spectrum. The new description allows us to interpret logarithmic TAQ as an abstract cotangent complex, and leads to an etale descent formula for logarithmic topological Hochschild homology. The latter is analogous to results of Weibel-Geller for Hochschild homology of discrete rings, and of McCarthy-Minasian and Mathew for topological Hochschild homology. We also summarize and clarify analogous results relating notions of formal etaleness defined in terms of ordinary THH and TAQ.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"39 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85899990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Matui's AH conjecture for graph groupoids 图群的Matui的AH猜想
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-03-31 DOI: 10.4171/dm/853
P. Nyland, E. Ortega
{"title":"Matui's AH conjecture for graph groupoids","authors":"P. Nyland, E. Ortega","doi":"10.4171/dm/853","DOIUrl":"https://doi.org/10.4171/dm/853","url":null,"abstract":"We prove that Matui's AH conjecture holds for graph groupoids of infinite graphs. This is a conjecture which relates the topological full group of an ample groupoid with the homology of the groupoid. Our main result complements Matui's result in the finite case, which makes the AH conjecture true for all graph groupoids covered by the assumptions of said conjecture. Furthermore, we observe that for arbitrary graphs, the homology of a graph groupoid coincides with the $K$-theory of its groupoid $C^*$-algebra.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"56 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83887357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Recovering a variable exponent 恢复一个可变指数
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-02-14 DOI: 10.25537/dm.2021v26.713-731
Tommi Brander, Jarkko Siltakoski
{"title":"Recovering a variable exponent","authors":"Tommi Brander, Jarkko Siltakoski","doi":"10.25537/dm.2021v26.713-731","DOIUrl":"https://doi.org/10.25537/dm.2021v26.713-731","url":null,"abstract":"We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using a Muntz-Szasz theorem after reducing the problem to determining a function from its $L^p$-norms.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"50 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73613669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators Toeplitz算子禁区内的分数指数衰减
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-01-22 DOI: 10.4171/dm/778
Alix Deleporte
{"title":"Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators","authors":"Alix Deleporte","doi":"10.4171/dm/778","DOIUrl":"https://doi.org/10.4171/dm/778","url":null,"abstract":"We prove several results of concentration for eigenfunctions in Toeplitz quantization. With mild assumptions on the regularity, we prove that eigenfunctions are $O(exp(-cN^{delta}))$ away from the corresponding level set of the symbol, where N is the inverse semiclassical parameter and $0 < delta < 1$ depends on the regularity. As an application, we prove a precise bound for the free energy of spin systems at high temperatures, sharpening a result of Lieb.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"8 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89064000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Frobenius and Spherical Codomains and Neighbourhoods Frobenius与球面上域和邻域
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-01-14 DOI: 10.25537/DM.2020V25.483-525
A. Hochenegger, C. Meachan
{"title":"Frobenius and Spherical Codomains and Neighbourhoods","authors":"A. Hochenegger, C. Meachan","doi":"10.25537/DM.2020V25.483-525","DOIUrl":"https://doi.org/10.25537/DM.2020V25.483-525","url":null,"abstract":"Given an exact functor between triangulated categories which admits both adjoints and whose cotwist is either zero or an autoequivalence, we show how to associate a unique full triangulated subcategory of the codomain on which the functor becomes either Frobenius or spherical, respectively. We illustrate our construction with examples coming from projective bundles and smooth blowups. This work generalises results about spherical subcategories obtained by Martin Kalck, David Ploog and the first author.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"85 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73099922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Norm-Compatible Systems of Galois Cohomology Classes for $mathbf{GSp}_6$ $mathbf{GSp}_6$的伽罗瓦上同调类的范数兼容系统
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-01-01 DOI: 10.4171/dm/767
Antonio Cauchi, Joaquín Rodrigues Jacinto
{"title":"Norm-Compatible Systems of Galois Cohomology Classes for $mathbf{GSp}_6$","authors":"Antonio Cauchi, Joaquín Rodrigues Jacinto","doi":"10.4171/dm/767","DOIUrl":"https://doi.org/10.4171/dm/767","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"33 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81104171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
Comparison Theory of Distance Spheres along Geodesics 距离球沿测地线的比较理论
IF 0.9 3区 数学
Documenta Mathematica Pub Date : 2020-01-01 DOI: 10.4171/dm/798
Reinhard Brocks
{"title":"Comparison Theory of Distance Spheres along Geodesics","authors":"Reinhard Brocks","doi":"10.4171/dm/798","DOIUrl":"https://doi.org/10.4171/dm/798","url":null,"abstract":"","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"8 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87526281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
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