Relevant bibliographies by topics / Arithmetic Riemann-Roch

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Arithmetic Riemann-Roch'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Arithmetic Riemann-Roch"

1

Gillet, Henri, and Christophe Soul�. "An arithmetic Riemann-Roch theorem." Inventiones Mathematicae 110, no. 1 (1992): 473–543. http://dx.doi.org/10.1007/bf01231343.

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Aitken, Wayne. "An arithmetic Riemann-Roch theorem for singular arithmetic surfaces." Memoirs of the American Mathematical Society 120, no. 573 (1996): 0. http://dx.doi.org/10.1090/memo/0573.

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Wüstholz, G. "LECTURES ON THE ARITHMETIC RIEMANN-ROCH THEOREM." Bulletin of the London Mathematical Society 26, no. 1 (1994): 111–12. http://dx.doi.org/10.1112/blms/26.1.111.

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Gillet, Henri, Damian Rössler, and Christophe Soulé. "An arithmetic Riemann-Roch theorem in higher degrees." Annales de l’institut Fourier 58, no. 6 (2008): 2169–89. http://dx.doi.org/10.5802/aif.2410.

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Freixas Montplet, Gérard. "An arithmetic Riemann-Roch theorem for pointed stable curves." Annales scientifiques de l'École normale supérieure 42, no. 2 (2009): 335–69. http://dx.doi.org/10.24033/asens.2098.

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Burgos Gil, José Ignacio, Gerard Freixas i Montplet, and Răzvan Liţcanu. "The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms." Annales de la faculté des sciences de Toulouse Mathématiques 23, no. 3 (2014): 513–59. http://dx.doi.org/10.5802/afst.1415.

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7

FREIXAS I MONTPLET, GERARD. "THE JACQUET–LANGLANDS CORRESPONDENCE AND THE ARITHMETIC RIEMANN–ROCH THEOREM FOR POINTED CURVES." International Journal of Number Theory 08, no. 01 (2012): 1–29. http://dx.doi.org/10.1142/s1793042112500017.

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We show how the Jacquet–Langlands correspondence and the arithmetic Riemann–Roch theorem for pointed curves, relate the arithmetic self-intersection numbers of the sheaves of modular forms — with their Petersson norms — on modular and Shimura curves: these are equal modulo ∑l∈S ℚ log l, where S is a controlled set of primes. These quantities were previously considered by Bost and Kühn (modular curve case) and Kudla–Rapoport–Yang and Maillot–Roessler (Shimura curve case). By the work of Maillot and Roessler, our result settles a question raised by Soulé.
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Tang, Shun. "An arithmetic Lefschetz–Riemann–Roch theorem." Proceedings of the London Mathematical Society, June 25, 2020. http://dx.doi.org/10.1112/plms.12349.

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9

"Riemann-Roch type theorems for arithmetic schemes with a finite group action." Journal für die reine und angewandte Mathematik (Crelles Journal) 1997, no. 489 (1997): 151–88. http://dx.doi.org/10.1515/crll.1997.489.151.

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CONNES, Alain, and Caterina CONSANI. "Segal’s Gamma rings and universal arithmetic." Quarterly Journal of Mathematics, December 15, 2020. http://dx.doi.org/10.1093/qmath/haaa042.

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Abstract Segal’s Γ-rings provide a natural framework for absolute algebraic geometry. We use G. Almkvist’s global Witt construction to explore the relation with J. Borger ${\mathbb F}_1$-geometry and compute the Witt functor-ring ${\mathbb W}_0({\mathbb S})$ of the simplest Γ-ring ${\mathbb S}$. We prove that it is isomorphic to the Galois invariant part of the BC-system, and exhibit the close relation between λ-rings and the Arithmetic Site. Then, we concentrate on the Arakelov compactification ${\overline{{\rm Spec\,}{\mathbb Z}}}$ which acquires a structure sheaf of ${\mathbb S}$-algebras.
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Dissertations / Theses on the topic "Arithmetic Riemann-Roch"

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Hahn, Tobias. "An arithmetic Riemann-Roch theorem for metrics with cusps." Aachen Shaker, 2009. http://d-nb.info/997223146/04.

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De, Gaetano Giovanni. "A regularized arithmetic Riemann-Roch theorem via metric degeneration." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19227.

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Das Hauptresultat dieser Arbeit ist ein regularisierter arithmetischer Satz von Riemann-Roch für ein hermitesches Geradenbündel, die isometrisch zum Geradenbündel den Spitzenformen vom geraden Gewicht ist, auf eine arithmetische Fläche, deren komplexe Faser isometrisch zu einer hyperbolischen Riemannschen Fläche ohne elliptische Punkte ist. Der Beweis des Resultats erfolgt durch metrische Degeneration: Wir regularisieren die betreffenden Metriken in einer Umgebung der Singularitäten, wenden dann den arithmetischen Riemann-Roch-Satz von Gillet und Soulé an und lassen schließlich den Paramete
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Hahn, Tobias [Verfasser]. "An arithmetic Riemann-Roch theorem for metrics with cusps / Tobias Hahn." Aachen : Shaker, 2009. http://d-nb.info/1156518318/34.

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Kramer, Jürg [Gutachter], and Gerard [Gutachter] Freixas. "A regularized arithmetic Riemann-Roch theorem via metric degeneration / Gutachter: Jürg Kramer, Gerard Freixas." Berlin : Humboldt-Universität zu Berlin, 2018. http://d-nb.info/1182540503/34.

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Usatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.

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If R is a list of positive integers with greatest common denominator equal to 1, calculating the Frobenius number of R is in general NP-hard. Dino Lorenzini defines the arithmetical graph, which naturally arises in arithmetic geometry, and a notion of genus, the g-number, that in specific cases coincides with the Frobenius number of R. A result of Dino Lorenzini's gives a method for quickly calculating upper bounds for the g-number of arithmetical graphs. We discuss the arithmetic geometry related to arithmetical graphs and present an example of an arithmetical graph that arises in this contex
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Ivey, law Hamish. "Algorithmic aspects of hyperelliptic curves and their jacobians." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4084/document.

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Ce travail se divise en deux parties. Dans la première partie, nous généralisons le travail de Khuri-Makdisi qui décrit des algorithmes pour l'arithmétique des diviseurs sur une courbe sur un corps. Nous montrons que les analogues naturelles de ses résultats se vérifient pour les diviseurs de Cartier relatifs effectifs sur un schéma projectif, lisse et de dimension relative un sur un schéma affine noetherien quelconque, et que les analogues naturelles de ses algorithmes se vérifient pour une certaine classe d'anneaux de base. Nous présentons un formalisme pour tels anneaux qui sont caractérisé
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Books on the topic "Arithmetic Riemann-Roch"

1

Aitken, Wayne. An arithmetic Riemann-Roch theorem for singular arithmetic surfaces. American Mathematical Society, 1996.

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2

Faltings, Gerd. Lectures on the arithmetic Riemann-Roch theorem. Princeton University Press, 1992.

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Bárcenas, Noé, and Monica Moreno Rocha. Mexican mathematicians abroad: Recent contributions : first workshop, Matematicos Mexicanos Jovenes en el Mundo, August 22-24, 2012, Centro de Investigacion en Matematicas, A.C., Guanajuato, Mexico. Edited by Galaz-García Fernando editor. American Mathematical Society, 2016.

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4

Faltings, Gerd. Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127. Princeton University Press, 2016.

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Book chapters on the topic "Arithmetic Riemann-Roch"

1

Bressler, Paul, Mikhail Kapranov, Boris Tsygan, and Eric Vasserot. "Riemann–Roch for Real Varieties." In Algebra, Arithmetic, and Geometry. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4745-2_4.

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Hulsbergen, Wilfred W. J. "Riemann-Roch, K-theory and motivic cohomology." In Conjectures in Arithmetic Algebraic Geometry. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-322-85466-7_5.

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Hulsbergen, Wilfred W. J. "Riemann-Roch, K-theory and motivic cohomology." In Conjectures in Arithmetic Algebraic Geometry. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-663-09505-7_5.

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Hirzebruch, F. "Arithmetic Genera And the Theorem of Riemann-Roch." In Teorema di Riemann-Roch e questioni connesse. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10889-1_3.

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Mumford, David. "The Arithmetic Genus and the Generalized Theorem of Riemann-Roch." In Algebraic Surfaces. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61991-5_4.

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Rössler, Damian. "A Local Refinement of the Adams–Riemann–Roch Theorem in Degree One." In Arithmetic L-Functions and Differential Geometric Methods. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65203-6_8.

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Montplet, Gerard Freixas i. "Chapter XI: The Arithmetic Riemann–Roch Theorem and the Jacquet–Langlands Correspondence." In Lecture Notes in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57559-5_12.

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Gramlich, Köhl né. "On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups." In Buildings, Finite Geometries and Groups. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0709-6_4.

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9

"The Arithmetic Riemann–Roch–Grothendieck Theorem." In Lectures on Arakelov Geometry. Cambridge University Press, 1992. http://dx.doi.org/10.1017/cbo9780511623950.011.

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"LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM." In Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127). Princeton University Press, 1992. http://dx.doi.org/10.1515/9781400882472-008.

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