Algebra, Arithmetic, and Geometry [electronic resource] : Volume I: In Honor of Yu. I. Manin / edited by Yuri Tschinkel, Yuri Zarhin.

Contributor(s): Tschinkel, Yuri [editor.] | Zarhin, Yuri [editor.] | SpringerLink (Online service)
Material type: TextTextSeries: Progress in Mathematics: 269Publisher: Boston : Birkhäuser Boston, 2009Description: XXXIV, 698 p. 41 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817647452Subject(s): Mathematics | Algebra | Algebraic geometry | Geometry | Number theory | Physics | Mathematics | Algebra | Number Theory | Geometry | Mathematical Methods in Physics | Algebraic GeometryAdditional physical formats: Printed edition:: No titleDDC classification: 512 LOC classification: QA150-272Online resources: Click here to access online
Contents:
Preface -- Introduction -- K. Behrend, B. Fantecci, Gerstenhaber and Batalin-Vilkovisky structures on Lagrangian intersections -- V. Berkovich, A non-Archimedean interpretation of the weight zero subspaces of limit mixed Hodge structures -- J.-B. Bost, A. Chambert-Loir, Analytic curves in algebraic varieties over number fields -- P. Bressler, M. Kapranov, B. Tsygan, E. Vasserot, Riemann-Roch for real varieties -- E. Colombo, B. van Geemen, E. Looijenga, Del Pezzo moduli via root systems -- A. Connes, C. Consani, M. Marcolli, The Weil proof and the geometry of the adeles class space -- A. Dabrowski, M. Wodzicki, Elliptic curves with large analytic III(E) -- C. Deninger, p-adic entropy and a p-adic Fuglede - Kadison determinant -- S. Donaldson, Lie algebra theory without algebra -- T. Ekedahl, G. van der Geer, Cycle classes of the E-O stratification on the moduli of abelian varieties -- A.-S. Elsenhans, J. Jahnel, Experiments with general cubic surfaces -- V.V. Fock, A. Goncharov, Cluster ensembles, quantization and the dilogarithm II: The intertwiner -- E. Getzler, Operads revisited -- M. Harris, Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications -- D. Kaledin, Cyclic homology with coefficients -- M. Kapranov, Noncommutative geometry and path integrals -- N. Katz, Another look at the Dwork family -- R. Kaufmann, Graphs, strings and actions -- J. Kollár, M. Larsen, Quotients of Calabi-Yau varieties -- M. Kontsevich, Notes on motives in finite characteristic -- L. Merel, Symboles de Manin et valeurs de fonctions L.-M. Markl, A. Voronov, PROPped up graph cohomology -- S. Merkulov, Graph complexes with loops and wheels -- M. Movshev, Yang-Mills theory and a superquadric -- E. Mukhin, V. Tarasov, A. Varchenko, A generalization of the Capelli identity -- J. Nekovar, Hidden symmetries of the theory of complex multiplication -- V. Nikulin, Correspondences of a K3 surface with itself via moduli of sheaves, I.-O. Ogievetsky, V. Schechtman, Uneintersection des quadriques liée à la suite de Sturm -- F. Oort, Foliations in moduli spaces of abelian varieties and dimension of leaves -- D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities -- A. Panchishkin, K. Vankov, Rankin's lemma of higher genus and explicit formulas for Hecke operators -- A. Polishchuk, Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations -- A. Vishik, Fields of $u$-invariant $2^r+1$ -- Y. Zarhin, Cubic surfaces and cubic threefolds, jacobians and intermediate jacobians -- Index.
In: Springer eBooksSummary: Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics. Contributors in the first volume include: K. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Da˛browski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.
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Preface -- Introduction -- K. Behrend, B. Fantecci, Gerstenhaber and Batalin-Vilkovisky structures on Lagrangian intersections -- V. Berkovich, A non-Archimedean interpretation of the weight zero subspaces of limit mixed Hodge structures -- J.-B. Bost, A. Chambert-Loir, Analytic curves in algebraic varieties over number fields -- P. Bressler, M. Kapranov, B. Tsygan, E. Vasserot, Riemann-Roch for real varieties -- E. Colombo, B. van Geemen, E. Looijenga, Del Pezzo moduli via root systems -- A. Connes, C. Consani, M. Marcolli, The Weil proof and the geometry of the adeles class space -- A. Dabrowski, M. Wodzicki, Elliptic curves with large analytic III(E) -- C. Deninger, p-adic entropy and a p-adic Fuglede - Kadison determinant -- S. Donaldson, Lie algebra theory without algebra -- T. Ekedahl, G. van der Geer, Cycle classes of the E-O stratification on the moduli of abelian varieties -- A.-S. Elsenhans, J. Jahnel, Experiments with general cubic surfaces -- V.V. Fock, A. Goncharov, Cluster ensembles, quantization and the dilogarithm II: The intertwiner -- E. Getzler, Operads revisited -- M. Harris, Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications -- D. Kaledin, Cyclic homology with coefficients -- M. Kapranov, Noncommutative geometry and path integrals -- N. Katz, Another look at the Dwork family -- R. Kaufmann, Graphs, strings and actions -- J. Kollár, M. Larsen, Quotients of Calabi-Yau varieties -- M. Kontsevich, Notes on motives in finite characteristic -- L. Merel, Symboles de Manin et valeurs de fonctions L.-M. Markl, A. Voronov, PROPped up graph cohomology -- S. Merkulov, Graph complexes with loops and wheels -- M. Movshev, Yang-Mills theory and a superquadric -- E. Mukhin, V. Tarasov, A. Varchenko, A generalization of the Capelli identity -- J. Nekovar, Hidden symmetries of the theory of complex multiplication -- V. Nikulin, Correspondences of a K3 surface with itself via moduli of sheaves, I.-O. Ogievetsky, V. Schechtman, Uneintersection des quadriques liée à la suite de Sturm -- F. Oort, Foliations in moduli spaces of abelian varieties and dimension of leaves -- D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities -- A. Panchishkin, K. Vankov, Rankin's lemma of higher genus and explicit formulas for Hecke operators -- A. Polishchuk, Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations -- A. Vishik, Fields of $u$-invariant $2^r+1$ -- Y. Zarhin, Cubic surfaces and cubic threefolds, jacobians and intermediate jacobians -- Index.

Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics. Contributors in the first volume include: K. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Da˛browski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.

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