Transactions of the American Mathematical Society, Series B最新文献

{"title":"Newton–Okounkov polytopes of flag varieties and marked chain-order polytopes","authors":"Naoki Fujita","doi":"10.1090/btran/142","DOIUrl":"https://doi.org/10.1090/btran/142","url":null,"abstract":"Marked chain-order polytopes are convex polytopes constructed from a marked poset. They give a discrete family relating a marked order polytope with a marked chain polytope. In this paper, we consider the Gelfand–Tsetlin poset of type \u0000\u0000 \u0000 A\u0000 A\u0000 \u0000\u0000, and realize the associated marked chain-order polytopes as Newton–Okounkov bodies of the flag variety. Our realization connects previous realizations of Gelfand–Tsetlin polytopes and Feigin–Fourier–Littelmann–Vinberg polytopes as Newton–Okounkov bodies in a uniform way. As an application, we prove that the flag variety degenerates into the irreducible normal projective toric variety corresponding to a marked chain-order polytope. We also construct a specific basis of an irreducible highest weight representation. The basis is naturally parametrized by the set of lattice points in a marked chain-order polytope.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130391734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bloch’s cycle complex and coherent dualizing complexes in positive characteristic","authors":"Fei Ren","doi":"10.1090/btran/119","DOIUrl":"https://doi.org/10.1090/btran/119","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be a separated scheme of dimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\">\u0000 <mml:semantics>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">d</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of finite type over a perfect field <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of positive characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In this work, we show that Bloch’s cycle complex <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z Subscript upper X Superscript c\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Z</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mi>c</mml:mi>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Z}^c_X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of zero cycles mod <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p Superscript n\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">p^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is quasi-isomorphic to the Cartier operator fixed part of a certain dualizing complex from coherent duality theory. From this we obtain new vanishing results for the higher Chow groups of zero cycles with mod <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p Superscript n\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">p^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> coefficients for singular varieties.</p>","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126964814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension","authors":"Satoshi Masaki, J. Segata, Kota Uriya","doi":"10.1090/btran/116","DOIUrl":"https://doi.org/10.1090/btran/116","url":null,"abstract":"In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems by the equivalence relation naturally induced by the linear transformation of the unknowns. It is revealed that the equivalence relation is well described by an identification with a matrix. In particular, we characterize some known systems in terms of the matrix and specify all systems equivalent to them. An explicit reduction procedure from a given system in the suitable subset to a model system, i.e., to a representative, is also established. The classification also draws our attention to some model systems which admit solutions with a new kind of asymptotic behavior. Especially, we find new systems which admit a solution of which decay rate is worse than that of a solution to the linear Klein-Gordon equation by logarithmic order.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128302515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hasse invariant for the tame Brauer group of a higher local field","authors":"E. Brussel","doi":"10.1090/btran/107","DOIUrl":"https://doi.org/10.1090/btran/107","url":null,"abstract":"We generalize the Hasse invariant of local class field theory to the tame Brauer group of a higher dimensional local field, and use it to study the arithmetic of central simple algebras, which are given a priori as tensor products of standard cyclic algebras. We also compute the tame Brauer dimension (or period-index bound) and the cyclic length of a general henselian-valued field of finite rank and finite residue field.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114767262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The operator system of Toeplitz matrices","authors":"D. Farenick","doi":"10.1090/btran/83","DOIUrl":"https://doi.org/10.1090/btran/83","url":null,"abstract":"<p>A recent paper of A. Connes and W.D. van Suijlekom [Comm. Math. Phys. 383 (2021), pp. 2021–2067] identifies the operator system of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The present paper examines this identification in somewhat more detail by showing explicitly that the Connes–van Suijlekom isomorphism is a unital complete order isomorphism of operator systems. Applications include two special results in matrix analysis: (i) that every positive linear map of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> complex matrices is completely positive when restricted to the operator subsystem of Toeplitz matrices and (ii) that every linear unital isometry of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Toeplitz matrices into the algebra of all <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> complex matrices is a unitary similarity transformation.</p>\u0000\u0000<p>An operator systems approach to Toeplitz matrices yields new insights into the positivity of block Toeplitz matrices, which are viewed herein as elements of tensor product spaces of an arbitrary operator system with the operator system of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130039246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the quotient of the homology cobordism group by Seifert spaces","authors":"Kristen Hendricks, Jennifer Hom, Matthew Stoffregen, Ian Zemke","doi":"10.1090/btran/110","DOIUrl":"https://doi.org/10.1090/btran/110","url":null,"abstract":"We prove that the quotient of the integer homology cobordism group by the subgroup generated by the Seifert fibered spaces is infinitely generated.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117286567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A universal Cannon-Thurston map and the surviving curve complex","authors":"Funda Gultepe, C. Leininger, Witsarut Pho-on","doi":"10.1090/btran/99","DOIUrl":"https://doi.org/10.1090/btran/99","url":null,"abstract":"Using the Birman exact sequence for pure mapping class groups, we construct a universal Cannon-Thurston map onto the boundary of a curve complex for a surface with punctures we call surviving curve complex. Along the way we prove hyperbolicity of this complex and identify its boundary as a space of laminations. As a corollary we obtain a universal Cannon-Thurston map to the boundary of the ordinary curve complex, extending earlier work of the second author with Mj and Schleimer [Comment. Math. Helv. 86 (2011), pp. 769–816].","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134475522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The heterotic 𝐺₂ system on contact Calabi–Yau 7-manifolds","authors":"Jason D. Lotay, H. S. Earp","doi":"10.1090/btran/129","DOIUrl":"https://doi.org/10.1090/btran/129","url":null,"abstract":"<p>We obtain non-trivial approximate solutions to the heterotic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper G 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {G}_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> system on the total spaces of non-trivial circle bundles over Calabi–Yau <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-orbifolds, which satisfy the equations up to an arbitrarily small error, by adjusting the size of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S Superscript 1\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">S^1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> fibres in proportion to a power of the string constant <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha prime\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mo>′</mml:mo>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha ’</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Each approximate solution provides a cocalibrated <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper G 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathrm {G}_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-structure, the torsion of which realises a non-trivial scalar field, a constant (trivial) dilaton field and an <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\">\u0000 <mml:semantics>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">H</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-flux with non-trivial Chern–Simons defect. The approximate solutions also include a connection on the tangent bundle which, together with a non-flat <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper G 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">G</mml:mi>\u0000 </mm","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124251503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On reflexive and 𝐼-Ulrich modules over curve singularities","authors":"Hailong Dao, Sarasij Maitra, P. Sridhar","doi":"10.1090/btran/96","DOIUrl":"https://doi.org/10.1090/btran/96","url":null,"abstract":"We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of \u0000\u0000 \u0000 I\u0000 I\u0000 \u0000\u0000-Ulrich modules.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129649743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Small deviations and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group","authors":"M. Carfagnini, M. Gordina","doi":"10.1090/btran/102","DOIUrl":"https://doi.org/10.1090/btran/102","url":null,"abstract":"A small ball problem and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion in Heisenberg group are proven. In addition, bounds on the limit in Chung’s law are established.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121484148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}