Documenta Mathematica最新文献_第7页

Finite groups scheme actions and incompressibility of Galois covers: beyond the ordinary case 有限群、方案作用和伽罗瓦覆盖的不可压缩性:超越一般情况

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-02-11 DOI: 10.4171/dm/868

N. Fakhruddin, Rijul Saini

引用次数: 3

The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields 虚二次域阿贝尔扩展的等变Tamagawa数猜想

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-02-02 DOI: 10.4171/dm/907

Dominik Bullach, Martin Hofer

引用次数: 2

Ricci DeTurck flow on incomplete manifolds 不完全流形上的Ricci DeTurck流

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-25 DOI: 10.4171/dm/894

Tobias Marxen, Boris Vertman

引用次数: 0

Towards a classification of connected components of the strata of $k$-differentials 关于k -微分地层连通分量的分类

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-05 DOI: 10.4171/dm/892

Dawei Chen, Q. Gendron

{"title":"Towards a classification of connected components of the strata of $k$-differentials","authors":"Dawei Chen, Q. Gendron","doi":"10.4171/dm/892","DOIUrl":"https://doi.org/10.4171/dm/892","url":null,"abstract":"A k-differential on a Riemann surface is a section of the k-th power of the canonical bundle. Loci of k-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification for the moduli space of k-differentials. The classification of connected components of the strata of k-differentials was known for holomorphic differentials, meromorphic differentials and quadratic differentials with at worst simple poles by Kontsevich–Zorich, Boissy and Lanneau, respectively. Built on their work we develop new techniques to study connected components of the strata of k-differentials for general k. As an application, we give a complete classification of connected components of the strata of quadratic differentials with arbitrary poles. Moreover, we distinguish certain components of the strata of kdifferentials by generalizing the hyperelliptic structure and spin parity for higher k. We also describe an approach to determine explicitly parities of k-differentials in genus zero and one, which inspires an amusing conjecture in number theory. A key viewpoint we use is the notion of multi-scale k-differentials introduced by Bainbridge– Chen–Gendron–Grushevsky–Möller for k = 1 and extended by Costantini–Möller– Zachhuber for all k.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88378470","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: 15

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior 具有规定约简行为的Severi-Brauer变种的代数连接K理论

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/820

Eoin Mackall

引用次数: 1

Erratum to: "The minimal exact crossed product" “最小精确交叉积”的勘误表

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/851

Alcides Buss, S. Echterhoff, R. Willett

引用次数: 0

Hecke $L$-functions and Fourier coefficients of covering Eisenstein series Hecke $L$-函数和覆盖爱森斯坦级数的傅里叶系数

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/819

Fan Gao

引用次数: 6

Torsors of isotropic reductive groups over Laurent polynomials 劳伦多项式上各向同性约化群的环量

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.25537/DM.2021V26.661-673

A. Stavrova

引用次数: 0

On the local regularity theory for the magnetohydrodynamic equations 磁流体动力学方程的局部正则性理论

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/811

D. Chamorro, F. Cortez, Jiao He, Oscar Jarŕın

引用次数: 1

On the James and Hilton-Milnor splittings, and the metastable EHP sequence 詹姆斯分裂和希尔顿-米尔诺分裂，以及亚稳态EHP序列

IF 0.9 3区数学

Documenta Mathematica Pub Date : 2021-01-01 DOI: 10.4171/dm/845

Sanath K. Devalapurkar, Peter J. Haine

{"title":"On the James and Hilton-Milnor splittings, and the metastable EHP sequence","authors":"Sanath K. Devalapurkar, Peter J. Haine","doi":"10.4171/dm/845","DOIUrl":"https://doi.org/10.4171/dm/845","url":null,"abstract":"This note provides modern proofs of some classical results in algebraic topology, such as the James Splitting, the Hilton–Milnor Splitting, and the metastable EHP sequence. We prove fundamental splitting results ΣΩΣX ≃ ΣX ∨ (X ∧ ΣΩΣX) and Ω(X ∨ Y ) ≃ ΩX × ΩY × ΩΣ(ΩX ∧ ΩY ) in the maximal generality of an ∞-category with finite limits and pushouts in which pushouts squares remain pushouts after basechange along an arbitrary morphism (i.e., Mather’s Second Cube Lemma holds). For connected objects, these imply the classical James and Hilton–Milnor Splittings. Moreover, working in this generality shows that the James and Hilton–Milnor splittings hold in many new contexts, for example in: elementary ∞-topoi, profinite spaces, and motivic spaces over arbitrary base schemes. The splitting results in this last context extend Wickelgren and Williams’ splitting result for motivic spaces over a perfect field. We also give two proofs of the metastable EHP sequence in the setting of ∞-topoi: the first is a new, non-computational proof that only utilizes basic connectedness estimates involving the James filtration and the Blakers–Massey Theorem, while the second reduces to the classical computational proof. 2020 Mathematics Subject Classification: 55P35, 55P40, 55P99, 55Q20, 18N60, 14F42","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88014671","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