Advances in Mathematics最新文献_第3页

First variation of functional Wulff shapes 功能伍尔夫形状的第一个变化

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-16 DOI: 10.1016/j.aim.2025.110529

Jacopo Ulivelli

引用次数: 0

Transfer principles for Galois cohomology and Serre's conjecture II 伽罗瓦上同调的转移原理与Serre猜想2

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-16 DOI: 10.1016/j.aim.2025.110532

Diego Izquierdo , Giancarlo Lucchini Arteche

引用次数: 0

Blow-ups and normal bundles in connective and nonconnective derived geometries 连接和非连接派生几何中的膨胀束和正常束

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-16 DOI: 10.1016/j.aim.2025.110530

Oren Ben-Bassat , Jeroen Hekking

{"title":"Blow-ups and normal bundles in connective and nonconnective derived geometries","authors":"Oren Ben-Bassat , Jeroen Hekking","doi":"10.1016/j.aim.2025.110530","DOIUrl":"10.1016/j.aim.2025.110530","url":null,"abstract":"<div><div>This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is our proposed globalization of a derived algebraic context, itself a generalization of the theory of simplicial commutative rings and due to Bhatt–Mathew and Raksit.</div><div>One key difference between a geometric context and ordinary derived algebraic geometry is that the coordinate ring of an affine object in the former is not necessarily connective. When constructing generalized blow-ups, this not only turns out to be remarkably convenient, but also leads to a wider existence result. Indeed, we show that the derived Rees algebra and the derived blow-up exist for any affine morphism of stacks in a given geometric context. However, in general the derived Rees algebra will no longer be connective, hence in general the derived blow-up will not live in the connective part of the theory. Unsurprisingly, this can be solved by restricting the input to closed immersions. The proof of the latter statement uses a derived deformation to the normal bundle in any given geometric context, which is also of independent interest.</div><div>Besides the geometric context which extends algebraic geometry, the second main example of a geometric context is an extension of analytic geometry as based on categories of Ind-Banach spaces or modules. The latter is a recent construction, and includes many different flavors of analytic geometry, such as complex analytic geometry, non-Archimedean rigid analytic geometry and analytic geometry over the integers. The present work thus provides derived blow-ups and a derived deformation to the normal bundle in all of these, which is expected to have many applications.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110530"},"PeriodicalIF":1.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

K-moduli spaces of log Del Pezzo pairs log Del Pezzo对的k模空间

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-12 DOI: 10.1016/j.aim.2025.110536

Long Pan , Fei Si , Haoyu Wu

引用次数: 0

Optimal version of the fundamental theorem of chronogeometry 时间几何基本定理的最佳版本

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-11 DOI: 10.1016/j.aim.2025.110528

Michiya Mori , Peter Šemrl

{"title":"Optimal version of the fundamental theorem of chronogeometry","authors":"Michiya Mori , Peter Šemrl","doi":"10.1016/j.aim.2025.110528","DOIUrl":"10.1016/j.aim.2025.110528","url":null,"abstract":"<div><div>We study lightlikeness preserving mappings from the 4-dimensional Minkowski spacetime <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> to itself under no additional regularity assumptions like continuity, surjectivity, or injectivity. We prove that such a mapping <em>ϕ</em> satisfies one of the following three conditions.<ul><li><span>(1)</span><span><div>The mapping <em>ϕ</em> can be written as a composition of a Lorentz transformation, a multiplication by a positive scalar, and a translation.</div></span></li><li><span>(2)</span><span><div>There is an event <span><math><mi>r</mi><mo>∈</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> such that <span><math><mi>ϕ</mi><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>∖</mo><mo>{</mo><mi>r</mi><mo>}</mo><mo>)</mo></math></span> is contained in one light cone.</div></span></li><li><span>(3)</span><span><div>There is a lightlike line <em>ℓ</em> such that <span><math><mi>ϕ</mi><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>∖</mo><mi>ℓ</mi><mo>)</mo></math></span> is contained in another lightlike line.</div></span></li></ul> Here, a line that is contained in some light cone in <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> is called a lightlike line. We also give several similar results on mappings defined on a certain subset of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> or the compactification of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110528"},"PeriodicalIF":1.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

A model for planar compacta and rational Julia sets 平面紧集与有理Julia集的一个模型

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-11 DOI: 10.1016/j.aim.2025.110531

Jun Luo , Yi Yang , Xiaoting Yao

{"title":"A model for planar compacta and rational Julia sets","authors":"Jun Luo , Yi Yang , Xiaoting Yao","doi":"10.1016/j.aim.2025.110531","DOIUrl":"10.1016/j.aim.2025.110531","url":null,"abstract":"<div><div>A <strong>Peano compactum</strong> means a compact metric space having locally connected components such that at most finitely many of them are of diameter greater than any fixed number <span><math><mi>C</mi><mo>></mo><mn>0</mn></math></span>. Given a compactum <em>K</em> in the extended complex plane <span><math><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>, it is known that there is a finest upper semi-continuous decomposition of <em>K</em> into subcontinua such that the resulting quotient space is a Peano compactum. We call this decomposition the <strong>core decomposition</strong> of <em>K</em> with Peano quotient and its elements <strong>atoms of</strong> <em>K</em>. We show that for any branched covering <span><math><mi>f</mi><mo>:</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>→</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> and any atom <em>d</em> of <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>K</mi><mo>)</mo></math></span>, the image <span><math><mi>f</mi><mo>(</mo><mi>d</mi><mo>)</mo></math></span> is an atom of <em>K</em>. Since rational functions are branched coverings, our result extends earlier ones that are restricted to more limited cases, requiring that <em>f</em> be a polynomial with <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>K</mi><mo>)</mo><mo>=</mo><mi>K</mi></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110531"},"PeriodicalIF":1.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Stable intersections of conformal regular Cantor sets with large Hausdorff dimensions 具有大Hausdorff维数的共形正则Cantor集的稳定交

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-11 DOI: 10.1016/j.aim.2025.110507

Hugo Araújo , Carlos Gustavo Moreira , Alex Zamudio Espinosa

引用次数: 0

Wondertopes Wondertopes

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-09-11 DOI: 10.1016/j.aim.2025.110516

Sarah Brauner , Christopher Eur , Elizabeth Pratt , Raluca Vlad

引用次数: 0

W⁎-superrigidity for groups with infinite center 具有无限中心群的W -超刚性