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Journal articles on the topic 'Riemann-Roch theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

Das, Mrinal Kanti, and Satya Mandal. "A Riemann–Roch theorem." Journal of Algebra 301, no. 1 (July 2006): 148–64. http://dx.doi.org/10.1016/j.jalgebra.2005.10.007.

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2

Hoyois, Marc, Pavel Safronov, Sarah Scherotzke, and Nicolò Sibilla. "The categorified Grothendieck–Riemann–Roch theorem." Compositio Mathematica 157, no. 1 (January 2021): 154–214. http://dx.doi.org/10.1112/s0010437x20007642.

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In this paper we prove a categorification of the Grothendieck–Riemann–Roch theorem. Our result implies in particular a Grothendieck–Riemann–Roch theorem for Toën and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the Toën–Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.

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3

Nori, Madhav V. "The Hirzebruch-Riemann-Roch theorem." Michigan Mathematical Journal 48, no. 1 (2000): 473–82. http://dx.doi.org/10.1307/mmj/1030132729.

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4

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

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5

Pappas, Georgios. "Integral Grothendieck–Riemann–Roch theorem." Inventiones mathematicae 170, no. 3 (July 18, 2007): 455–81. http://dx.doi.org/10.1007/s00222-007-0067-9.

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6

Navarro, Alberto. "On Grothendieck’s Riemann–Roch theorem." Expositiones Mathematicae 35, no. 3 (September 2017): 326–42. http://dx.doi.org/10.1016/j.exmath.2016.09.005.

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7

Paule, Peter, and Cristian-Silviu Radu. "A Proof of the Weierstraß Gap Theorem not Using the Riemann–Roch Formula." Annals of Combinatorics 23, no. 3-4 (November 2019): 963–1007. http://dx.doi.org/10.1007/s00026-019-00459-2.

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Abstract Usually, the Weierstraß gap theorem is derived as a straightforward corollary of the Riemann–Roch theorem. Our main objective in this article is to prove the Weierstraß gap theorem by following an alternative approach based on “first principles”, which does not use the Riemann–Roch formula. Having mostly applications in connection with modular functions in mind, we describe our approach for the case when the given compact Riemann surface is associated with the modular curve $$X_0(N)$$X0(N).

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8

JØRGENSEN, PETER. "NON-COMMUTATIVE CURVES AND THEIR ZETA FUNCTIONS." Journal of Algebra and Its Applications 01, no. 02 (June 2002): 175–99. http://dx.doi.org/10.1142/s0219498802000094.

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This paper considers non-commutative curves, introduces a divisor class group and a degree map, proves a Riemann-Roch theorem, and solves the Riemann-Roch problem. These results are then used to prove the zeta function of a non-commutative curve over a finite field satisfies the two first Weil conjectures.

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9

Douglas, Ronald G., Xiang Tang, and Guoliang Yu. "An analytic Grothendieck Riemann Roch theorem." Advances in Mathematics 294 (May 2016): 307–31. http://dx.doi.org/10.1016/j.aim.2016.02.031.

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10

Ramadoss, Ajay C. "A generalized Hirzebruch Riemann–Roch theorem." Comptes Rendus Mathematique 347, no. 5-6 (March 2009): 289–92. http://dx.doi.org/10.1016/j.crma.2009.01.015.

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11

Tsiganov, A. V. "Superintegrable systems and Riemann-Roch theorem." Journal of Mathematical Physics 61, no. 1 (January 1, 2020): 012701. http://dx.doi.org/10.1063/1.5132869.

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12

Cangelmi, Leonardo. "A Riemann–Roch theorem for hypermaps." European Journal of Combinatorics 33, no. 7 (October 2012): 1444–48. http://dx.doi.org/10.1016/j.ejc.2012.03.009.

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13

Merkl, Franz. "A Riemann Roch Theorem for infinite genus Riemann surfaces." Inventiones mathematicae 139, no. 2 (February 2000): 391–437. http://dx.doi.org/10.1007/s002229900031.

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14

Lesfari, A. "Riemann-Roch theorem and Kodaira-Serre duality." Annals of West University of Timisoara - Mathematics and Computer Science 58, no. 1 (June 1, 2022): 4–17. http://dx.doi.org/10.2478/awutm-2022-0002.

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Abstract The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of this paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces.

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15

Ando, Tetsuya. "The Riemann-Roch theorem and Bernoulli polynomials." Proceedings of the Japan Academy, Series A, Mathematical Sciences 61, no. 6 (1985): 161–63. http://dx.doi.org/10.3792/pjaa.61.161.

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16

Petit, François. "A Riemann-Roch theorem for dg algebras." Bulletin de la Société mathématique de France 141, no. 2 (2013): 197–223. http://dx.doi.org/10.24033/bsmf.2646.

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17

Schröder, Herbert. "The Riemann-Roch theorem on algebraic curves." Séminaire de théorie spectrale et géométrie 7 (1989): 115–21. http://dx.doi.org/10.5802/tsg.70.

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18

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

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19

Wang, ShiKun, and HuiPing Zhang. "An application of the Riemann-Roch theorem." Science in China Series A: Mathematics 51, no. 4 (April 2008): 765–72. http://dx.doi.org/10.1007/s11425-007-0160-y.

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20

Levy, Roni N. "The Riemann-Roch theorem for complex spaces." Acta Mathematica 158 (1987): 149–88. http://dx.doi.org/10.1007/bf02392258.

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21

Mori, Izuru. "Riemann–Roch like theorem for triangulated categories." Journal of Pure and Applied Algebra 193, no. 1-3 (October 2004): 263–85. http://dx.doi.org/10.1016/j.jpaa.2004.03.008.

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22

Osipov, D. V., and A. N. Parshin. "Harmonic analysis and the Riemann-Roch theorem." Doklady Mathematics 84, no. 3 (December 2011): 826–29. http://dx.doi.org/10.1134/s106456241107026x.

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23

Brzezinski, J. "Riemann-Roch theorem for locally principal orders." Mathematische Annalen 276, no. 4 (December 1987): 529–36. http://dx.doi.org/10.1007/bf01456982.

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24

Gathmann, Andreas, and Michael Kerber. "A Riemann–Roch theorem in tropical geometry." Mathematische Zeitschrift 259, no. 1 (July 19, 2007): 217–30. http://dx.doi.org/10.1007/s00209-007-0222-4.

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25

KACHKACHI, H., and M. KACHKACHI. "SUPERCONFORMAL STRUCTURES AND HOLOMORPHIC 1/2-SUPERDIFFERENTIALS ON N=1 SUPER RIEMANN SURFACES." Modern Physics Letters A 08, no. 38 (December 14, 1993): 3643–58. http://dx.doi.org/10.1142/s0217732393002385.

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Using the super Riemann-Roch theorem we give a local expression for a holomorphic ½-superdifferential in a superconformal structure parametrized by special isothermal coordinates on an N=1 super Riemann surface. The holomorphy of these coordinates with respect to super Beltrami differentials is proved. The monodromy of these differentials is discussed.

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26

James, Rodney, and Rick Miranda. "A Riemann-Roch theorem for edge-weighted graphs." Proceedings of the American Mathematical Society 141, no. 11 (July 26, 2013): 3793–802. http://dx.doi.org/10.1090/s0002-9939-2013-11671-0.

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27

Roessler, Damian. "An Adams-Riemann-Roch theorem in Arakelov geometry." Duke Mathematical Journal 96, no. 1 (January 1999): 61–126. http://dx.doi.org/10.1215/s0012-7094-99-09603-5.

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28

Thomason, R. W. "Lefschetz-Riemann-Roch theorem and coherent trace formula." Inventiones Mathematicae 85, no. 3 (October 1986): 515–43. http://dx.doi.org/10.1007/bf01390328.

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29

Wang, Hongyu, and Peng Zhu. "Local Riemann-Roch theorem for almost Hermitian manifolds." Bulletin of the Brazilian Mathematical Society, New Series 41, no. 4 (November 7, 2010): 583–605. http://dx.doi.org/10.1007/s00574-010-0027-7.

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30

Takeda, Yuichiro. "Lefschetz-Riemann-Roch theorem for smooth algebraic schemes." Mathematische Zeitschrift 211, no. 1 (December 1992): 643–56. http://dx.doi.org/10.1007/bf02571452.

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31

Li, Dinping, and Stéphane Ouvry. "Haldane's fractional statistics and the Riemann-Roch theorem." Nuclear Physics B 430, no. 3 (November 1994): 563–76. http://dx.doi.org/10.1016/0550-3213(94)90159-7.

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32

Madsen, Ib. "An integral Riemann–Roch theorem for surface bundles." Advances in Mathematics 225, no. 6 (December 2010): 3229–57. http://dx.doi.org/10.1016/j.aim.2010.06.001.

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33

Levy, Roni N. "Riemann-Roch theorem for higher bivariant K-functors." Annales de l’institut Fourier 58, no. 2 (2008): 571–601. http://dx.doi.org/10.5802/aif.2361.

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34

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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35

Shubin, M. A. "L 2 Riemann-Roch theorem for elliptic operators." Geometric and Functional Analysis 5, no. 2 (March 1995): 482–527. http://dx.doi.org/10.1007/bf01895677.

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36

Blache, R. "Riemann-Roch theorem for normal surfaces and applications." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 65, no. 1 (December 1995): 307–40. http://dx.doi.org/10.1007/bf02953338.

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37

Rump, Wolfgang. "Frobenius Quantales, Serre Quantales and the Riemann–Roch Theorem." Studia Logica 110, no. 2 (October 18, 2021): 405–27. http://dx.doi.org/10.1007/s11225-021-09970-1.

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38

Kondyrev, Grigory, and Artem Prikhodko. "Equivariant Grothendieck–Riemann–Roch theorem via formal deformation theory." Cambridge Journal of Mathematics 9, no. 4 (2021): 809–99. http://dx.doi.org/10.4310/cjm.2021.v9.n4.a1.

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39

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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40

KOCK, B. "The Grothendieck-Riemann-Roch theorem for group scheme actions." Annales Scientifiques de l’École Normale Supérieure 31, no. 3 (May 1998): 415–58. http://dx.doi.org/10.1016/s0012-9593(98)80140-7.

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41

Perrot, Denis. "A Riemann-Roch Theorem¶for One-Dimensional Complex Groupoids." Communications in Mathematical Physics 218, no. 2 (April 1, 2001): 373–91. http://dx.doi.org/10.1007/s002200100404.

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42

Khalkhali, Masoud, and Ali Moatadelro. "A Riemann–Roch theorem for the noncommutative two torus." Journal of Geometry and Physics 86 (December 2014): 19–30. http://dx.doi.org/10.1016/j.geomphys.2014.06.005.

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43

Ho, Man-Ho. "The flat Grothendieck–Riemann–Roch theorem without adiabatic techniques." Journal of Geometry and Physics 107 (September 2016): 162–74. http://dx.doi.org/10.1016/j.geomphys.2016.05.016.

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44

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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45

Pink, Richard, and Damian Rössler. "On the Adams–Riemann–Roch theorem in positive characteristic." Mathematische Zeitschrift 270, no. 3-4 (April 9, 2011): 1067–76. http://dx.doi.org/10.1007/s00209-011-0841-7.

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46

Kurano, Kazuhiko. "The singular Riemann–Roch theorem and Hilbert–Kunz functions." Journal of Algebra 304, no. 1 (October 2006): 487–99. http://dx.doi.org/10.1016/j.jalgebra.2005.11.019.

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47

Markarian, Nikita. "The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem." Journal of the London Mathematical Society 79, no. 1 (October 9, 2008): 129–43. http://dx.doi.org/10.1112/jlms/jdn064.

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48

Prokhorov, Yu G., and A. B. Verëvkin. "The Riemann-Roch theorem on surfaces with log-terminal singularities." Journal of Mathematical Sciences 140, no. 2 (January 2007): 200–205. http://dx.doi.org/10.1007/s10958-007-0417-6.

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49

Mathai, Varghese, and Jonathan Rosenberg. "The Riemann–Roch Theorem on higher dimensional complex noncommutative tori." Journal of Geometry and Physics 147 (January 2020): 103534. http://dx.doi.org/10.1016/j.geomphys.2019.103534.

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50

Ho, Man-Ho. "A condensed proof of the differential Grothendieck–Riemann–Roch theorem." Proceedings of the American Mathematical Society 142, no. 6 (March 12, 2014): 1973–82. http://dx.doi.org/10.1090/s0002-9939-2014-11948-4.

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