Mathematische Annalen最新文献

{"title":"Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups.","authors":"Petr Naryshkin, Andrea Vaccaro","doi":"10.1007/s00208-024-03075-5","DOIUrl":"https://doi.org/10.1007/s00208-024-03075-5","url":null,"abstract":"<p><p>We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit moreover to show that every such action has finite Borel asymptotic dimension.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"197-208"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971200/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Splitting unramified Brauer classes by abelian torsors and the period-index problem.","authors":"Daniel Huybrechts, Dominique Mattei","doi":"10.1007/s00208-025-03161-2","DOIUrl":"10.1007/s00208-025-03161-2","url":null,"abstract":"<p><p>We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power of its period.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 2","pages":"2913-2932"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084267/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144094321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials.","authors":"Alexander Ulanovskii, Ilya Zlotnikov","doi":"10.1007/s00208-024-03011-7","DOIUrl":"https://doi.org/10.1007/s00208-024-03011-7","url":null,"abstract":"<p><p>We introduce two families of generators (functions) <math><mi>G</mi></math> that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 3","pages":"3429-3456"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11829847/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143441152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions.","authors":"Arturo Espinosa Baro, Michael Farber, Stephan Mescher, John Oprea","doi":"10.1007/s00208-024-03033-1","DOIUrl":"https://doi.org/10.1007/s00208-024-03033-1","url":null,"abstract":"<p><p>We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 3","pages":"4555-4605"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11829864/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143441159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the best constants of Schur multipliers of second order divided difference functions.","authors":"Martijn Caspers, Jesse Reimann","doi":"10.1007/s00208-025-03111-y","DOIUrl":"https://doi.org/10.1007/s00208-025-03111-y","url":null,"abstract":"<p><p>We give a new proof of the boundedness of bilinear Schur multipliers of second order divided difference functions, as obtained earlier by Potapov, Skripka and Sukochev in their proof of Koplienko's conjecture on the existence of higher order spectral shift functions. Our proof is based on recent methods involving bilinear transference and the Hörmander-Mikhlin-Schur multiplier theorem. Our approach provides a significant sharpening of the known asymptotic bounds of bilinear Schur multipliers of second order divided difference functions. Furthermore, we give a new lower bound of these bilinear Schur multipliers, giving again a fundamental improvement on the best known bounds obtained by Coine, Le Merdy, Potapov, Sukochev and Tomskova. More precisely, we prove that for <math><mrow><mi>f</mi> <mo>∈</mo> <msup><mi>C</mi> <mn>2</mn></msup> <mrow><mo>(</mo> <mi>R</mi> <mo>)</mo></mrow> </mrow> </math> and <math><mrow><mn>1</mn> <mo><</mo> <mi>p</mi> <mo>,</mo> <msub><mi>p</mi> <mn>1</mn></msub> <mo>,</mo> <msub><mi>p</mi> <mn>2</mn></msub> <mo><</mo> <mi>∞</mi></mrow> </math> with <math> <mrow><mfrac><mn>1</mn> <mi>p</mi></mfrac> <mo>=</mo> <mfrac><mn>1</mn> <msub><mi>p</mi> <mn>1</mn></msub> </mfrac> <mo>+</mo> <mfrac><mn>1</mn> <msub><mi>p</mi> <mn>2</mn></msub> </mfrac> </mrow> </math> we have <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><mrow><mo>‖</mo></mrow> <msub><mi>M</mi> <msup><mi>f</mi> <mrow><mo>[</mo> <mn>2</mn> <mo>]</mo></mrow> </msup> </msub> <mo>:</mo> <msub><mi>S</mi> <msub><mi>p</mi> <mn>1</mn></msub> </msub> <mo>×</mo> <msub><mi>S</mi> <msub><mi>p</mi> <mn>2</mn></msub> </msub> <mo>→</mo> <msub><mi>S</mi> <mi>p</mi></msub> <mrow><mo>‖</mo> <mo>≲</mo> <mo>‖</mo></mrow> <msup><mi>f</mi> <mrow><mo>'</mo> <mo>'</mo></mrow> </msup> <msub><mrow><mo>‖</mo></mrow> <mi>∞</mi></msub> <mi>D</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>,</mo> <msub><mi>p</mi> <mn>1</mn></msub> <mo>,</mo> <msub><mi>p</mi> <mn>2</mn></msub> <mo>)</mo></mrow> <mo>,</mo></mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> where the constant <math><mrow><mi>D</mi> <mo>(</mo> <mi>p</mi> <mo>,</mo> <msub><mi>p</mi> <mn>1</mn></msub> <mo>,</mo> <msub><mi>p</mi> <mn>2</mn></msub> <mo>)</mo></mrow> </math> is specified in Theorem 7.1 and <math><mrow><mi>D</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>,</mo> <mn>2</mn> <mi>p</mi> <mo>,</mo> <mn>2</mn> <mi>p</mi> <mo>)</mo></mrow> <mo>≈</mo> <msup><mi>p</mi> <mn>4</mn></msup> <msup><mi>p</mi> <mo>∗</mo></msup> </mrow> </math> with <math><msup><mi>p</mi> <mo>∗</mo></msup> </math> the Hölder conjugate of <i>p</i>. We further show that for <math><mrow><mi>f</mi> <mo>(</mo> <mi>λ</mi> <mo>)</mo> <mo>=</mo> <mi>λ</mi> <mo>|</mo> <mi>λ</mi> <mo>|</mo> <mo>,</mo></mrow> </math> <math><mrow><mi>λ</mi> <mo>∈</mo> <mi>R</mi> <mo>,</mo></mrow> </math> for every <math><mrow><mn>1</mn> <mo><</mo> <mi>p</mi> <mo><</mo> <mi>∞</mi></mrow> </math> we have <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><msup><mi>p</mi> <mn>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"1119-1166"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971180/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial Fourier decay for fractal measures and their pushforwards.","authors":"Simon Baker, Amlan Banaji","doi":"10.1007/s00208-025-03091-z","DOIUrl":"https://doi.org/10.1007/s00208-025-03091-z","url":null,"abstract":"<p><p>We prove that the pushforwards of a very general class of fractal measures <math><mi>μ</mi></math> on <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> under a large family of non-linear maps <math><mrow><mi>F</mi> <mo>:</mo> <mspace></mspace> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> <mo>→</mo> <mi>R</mi></mrow> </math> exhibit polynomial Fourier decay: there exist <math><mrow><mi>C</mi> <mo>,</mo> <mi>η</mi> <mo>></mo> <mn>0</mn></mrow> </math> such that <math> <mrow><mrow><mo>|</mo></mrow> <mover><mrow><mi>F</mi> <mi>μ</mi></mrow> <mo>^</mo></mover> <msup> <mrow><mrow><mo>(</mo> <mi>ξ</mi> <mo>)</mo></mrow> <mo>|</mo> <mo>≤</mo> <mi>C</mi> <mo>|</mo> <mi>ξ</mi> <mo>|</mo></mrow> <mrow><mo>-</mo> <mi>η</mi></mrow> </msup> </mrow> </math> for all <math><mrow><mi>ξ</mi> <mo>≠</mo> <mn>0</mn></mrow> </math> . Using this, we prove that if <math><mrow><mi>Φ</mi> <mo>=</mo> <msub><mrow><mo>{</mo> <msub><mi>φ</mi> <mi>a</mi></msub> <mo>:</mo> <mspace></mspace> <mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo></mrow> <mo>→</mo> <mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo></mrow> <mo>}</mo></mrow> <mrow><mi>a</mi> <mo>∈</mo> <mi>A</mi></mrow> </msub> </mrow> </math> is an iterated function system consisting of analytic contractions, and there exists <math><mrow><mi>a</mi> <mo>∈</mo> <mi>A</mi></mrow> </math> such that <math><msub><mi>φ</mi> <mi>a</mi></msub> </math> is not an affine map, then every non-atomic self-conformal measure for <math><mi>Φ</mi></math> has polynomial Fourier decay; this result was obtained simultaneously by Algom, Rodriguez Hertz, and Wang. We prove applications related to the Fourier uniqueness problem, Fractal Uncertainty Principles, Fourier restriction estimates, and quantitative equidistribution properties of numbers in fractal sets.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"209-261"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971211/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantitative approximate definable choices.","authors":"Antonio Lerario, Luca Rizzi, Daniele Tiberio","doi":"10.1007/s00208-025-03128-3","DOIUrl":"https://doi.org/10.1007/s00208-025-03128-3","url":null,"abstract":"<p><p>In semialgebraic geometry, projections play a prominent role. A <i>definable choice</i> is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends exponentially on the number of variables. By allowing the selection to be approximate (in the Hausdorff sense), we improve on this result. In particular, we construct an approximate selection whose degree is linear in the complexity of the projection and does not depend on the number of variables. This work is motivated by infinite-dimensional applications, in particular to the Sard conjecture in sub-Riemannian geometry. To prove these results, we develop a general quantitative theory for Hausdorff approximations in semialgebraic geometry, which has independent interest.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"1289-1319"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971197/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classicality of derived Emerton-Gee stack.","authors":"Yu Min","doi":"10.1007/s00208-025-03259-7","DOIUrl":"https://doi.org/10.1007/s00208-025-03259-7","url":null,"abstract":"<p><p>We construct a derived stack <math><mi>X</mi></math> of Laurent <i>F</i>-crystals on , where <math><msub><mi>O</mi> <mi>K</mi></msub> </math> is the ring of integers of a finite extension <i>K</i> of <math><msub><mi>Q</mi> <mi>p</mi></msub> </math> . We first show that its underlying classical stack <math> <mrow><mmultiscripts><mrow></mrow> <mrow></mrow> <mtext>cl</mtext></mmultiscripts> <mi>X</mi></mrow> </math> coincides with the Emerton-Gee stack <math><msub><mi>X</mi> <mtext>EG</mtext></msub> </math> , i.e. the moduli stack of étale <math><mrow><mo>(</mo> <mi>φ</mi> <mo>,</mo> <mi>Γ</mi> <mo>)</mo></mrow> </math> -modules. Then we prove that the derived stack <math><mi>X</mi></math> is classical in the sense that when restricted to truncated animated rings, <math><mi>X</mi></math> is equivalent to the sheafification of the left Kan extension of <math><msub><mi>X</mi> <mtext>EG</mtext></msub> </math> along the inclusion from the classical commutative rings to animated rings.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 1","pages":"439-494"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12488806/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145233005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\"><ns0:math><ns0:msup><ns0:mi>C</ns0:mi> <ns0:mi>∞</ns0:mi></ns0:msup> </ns0:math> regularity in semilinear free boundary problems.","authors":"Daniel Restrepo, Xavier Ros-Oton","doi":"10.1007/s00208-025-03135-4","DOIUrl":"10.1007/s00208-025-03135-4","url":null,"abstract":"<p><p>We study the higher regularity of solutions and free boundaries in the Alt-Phillips problem <math><mrow><mi>Δ</mi> <mi>u</mi> <mo>=</mo> <msup><mi>u</mi> <mrow><mi>γ</mi> <mo>-</mo> <mn>1</mn></mrow> </msup> <mo>,</mo></mrow> </math> with <math><mrow><mi>γ</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> <mo>.</mo></mrow> </math> Our main results imply that, once free boundaries are <math> <mrow><msup><mi>C</mi> <mrow><mn>1</mn> <mo>,</mo> <mi>α</mi></mrow> </msup> <mo>,</mo></mrow> </math> then they are <math> <mrow><msup><mi>C</mi> <mi>∞</mi></msup> <mo>.</mo></mrow> </math> In addition <math><mrow><mi>u</mi> <mo>/</mo> <msup><mi>d</mi> <mfrac><mn>2</mn> <mrow><mn>2</mn> <mo>-</mo> <mi>γ</mi></mrow> </mfrac> </msup> </mrow> </math> and <math><msup><mi>u</mi> <mfrac><mrow><mn>2</mn> <mo>-</mo> <mi>γ</mi></mrow> <mn>2</mn></mfrac> </msup> </math> are <math><msup><mi>C</mi> <mi>∞</mi></msup> </math> too. In order to achieve this, we need to establish fine regularity estimates for solutions of linear equations with boundary-singular Hardy potentials <math><mrow><mo>-</mo> <mi>Δ</mi> <mi>v</mi> <mo>=</mo> <mi>κ</mi> <mi>v</mi> <mo>/</mo> <msup><mi>d</mi> <mn>2</mn></msup> </mrow> </math> in <math><mrow><mi>Ω</mi> <mo>,</mo></mrow> </math> where <i>d</i> is the distance to the boundary and <math><mrow><mi>κ</mi> <mo>≤</mo> <mfrac><mn>1</mn> <mn>4</mn></mfrac> <mo>.</mo></mrow> </math> Interestingly, we need to include even the critical constant <math><mrow><mi>κ</mi> <mo>=</mo> <mfrac><mn>1</mn> <mn>4</mn></mfrac> <mo>,</mo></mrow> </math> which corresponds to <math><mrow><mi>γ</mi> <mo>=</mo> <mfrac><mn>2</mn> <mn>3</mn></mfrac> <mo>.</mo></mrow></math></p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3397-3446"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310783/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the smooth locus of affine Schubert varieties.","authors":"Georgios Pappas, Rong Zhou","doi":"10.1007/s00208-025-03123-8","DOIUrl":"https://doi.org/10.1007/s00208-025-03123-8","url":null,"abstract":"<p><p>We give a simple and uniform proof of a conjecture of Haines-Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 2","pages":"1483-1501"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084183/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144094315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}