Inventiones mathematicae

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• Semi-simplicity of tensorial products in characteristics p AI翻译
  作者：Deligne, Pierre
  作者单位：Institute for Advanced Study - USA
• Local cohomology modules of a smooth Z-algebra have finitely many associated primes AI翻译
  作者：Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
  作者单位：Institute for Advanced Study - USA; Johannes Gutenberg University of Mainz; University of Minnesota System; University of Minnesota Twin Cities; Utah System of Higher Education; University of Utah; University of Nebraska System; University of Nebraska Lincoln
  摘要：Let R be a commutative Noetherian ring that is a smooth -algebra. For each ideal of R and integer k, we prove that the local cohomology module has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.
• Large outlying stable constant mean curvature spheres in initial data sets AI翻译
  作者：Brendle, Simon; Eichmair, Michael
  作者单位：Stanford University; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We give examples of asymptotically flat three-manifolds which admit arbitrarily large constant mean curvature spheres that are far away from the center of the manifold. This resolves a question raised by Huisken and Yau (Invent Math 124:281-311, 1996). On the other hand, we show that such surfaces cannot exist when has nonnegative scalar curvature. This result depends on an intricate relationship between the scalar curvature of the initial data set and the isoperimetric ratio of large stable c...
• Motives with exceptional Galois groups and the inverse Galois problem AI翻译
  作者：Yun, Zhiwei
  作者单位：Stanford University
  摘要：We construct motivic a-adic representations of into exceptional groups of type E (7),E (8) and G (2) whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and is inspired by the Langlands correspondence for function fields. As an application, we solve new cases of the inverse Galois problem: the finite simple groups are Galois groups over for large enough primes a.
• KP solitons and total positivity for the Grassmannian AI翻译
  作者：Kodama, Yuji; Williams, Lauren
  作者单位：University System of Ohio; Ohio State University; University of California System; University of California Berkeley
  摘要：Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to construct a soliton solution to the KP equation from each point of the real Grassmannian Gr(k,n). More recently, several authors (Biondini and Chakravarty, J Math Phys 47:033514, 2006; Biondini and Kodama, J. Phys A Math Gen 36:10519-10536, 2003; Ch...
• True trees are dense AI翻译
  作者：Bishop, Christopher J.
  作者单位：State University of New York (SUNY) System; Stony Brook University
  摘要：We show that any compact, connected set K in the plane can be approximated by the critical points of a polynomial with two critical values. Equivalently, K can be approximated in the Hausdorff metric by a true tree in the sense of Grothendieck's dessins d'enfants.
• Monodromy of cyclic coverings of the projective line AI翻译
  作者：Venkataramana, T. N.
  作者单位：Tata Institute of Fundamental Research (TIFR)
  摘要：We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of ramification points is sufficiently large compared to the degree d and the ramification degrees are co-prime to d.
• On uniqueness of tangent cones for Einstein manifolds AI翻译
  作者：Colding, Tobias Holck; Minicozzi, William P., II
  作者单位：Massachusetts Institute of Technology (MIT); Johns Hopkins University
  摘要：We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.
• A fully anisotropic mechanism for formation of trapped surfaces in vacuum AI翻译
  作者：Klainerman, Sergiu; Luk, Jonathan; Rodnianski, Igor
  作者单位：Princeton University; University of Pennsylvania; Massachusetts Institute of Technology (MIT)
  摘要：We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide local conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat in all other directions) whose future development contains a trapped surface. This extends considerably the previous result of Christodoulou (Monographs in Mathematics. European Mathematical Society, Switzerland, 2009) which required instead a uniform condition along al...
• Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations AI翻译
  作者：Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
  作者单位：University of Kansas; Universite Claude Bernard Lyon 1; Indiana University System; Indiana University Bloomington
  摘要：We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time behavior is governed by an associated second-order formal Whitham modulation system. A key point is to identify the way in which initial perturbations translate to initial data for this formal system, a task accomplished by detailed estimates on the linearized ...