{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T14:14:12Z","timestamp":1776694452606,"version":"3.51.2"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[1996,7,1]],"date-time":"1996-07-01T00:00:00Z","timestamp":836179200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[1996,7]]},"DOI":"10.1007\/bf01195534","type":"journal-article","created":{"date-parts":[[2005,2,18]],"date-time":"2005-02-18T11:10:49Z","timestamp":1108725049000},"page":"289-298","source":"Crossref","is-referenced-by-count":8,"title":["Weil bounds for singular curves"],"prefix":"10.1007","volume":"7","author":[{"given":"Eric","family":"Bach","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF01195534_CR1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0022-0000(91)90038-7","volume":"42","author":"E. Bach","year":"1991","unstructured":"Bach, E.: Realistic analysis of some randomized algorithms. J. Comput. Sys. Sci.42, 30\u201352 (1991)","journal-title":"J. Comput. Sys. Sci."},{"key":"BF01195534_CR2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0890-5401(91)90001-I","volume":"90","author":"E. Bach","year":"1991","unstructured":"Bach, E.: Toward a theory of Pollard's rho method. Inf. Comput.90, 139\u2013155 (1991)","journal-title":"Inf. Comput."},{"key":"BF01195534_CR3","unstructured":"Eisenbud, D., Harris, J.: Schemes: The Language of Modern Algebraic Geometry. Wadsworth & Brooks\/Cole 1992"},{"key":"BF01195534_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-07216-5","volume-title":"Field Arithmetic","author":"M. D. Fried","year":"1986","unstructured":"Fried, M. D., Jarden, M.: Field Arithmetic. Springer Berlin 1986"},{"key":"BF01195534_CR5","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1090\/S0002-9947-1952-0049591-8","volume":"72","author":"D. Gorenstein","year":"1952","unstructured":"Gorenstein, D.: An arithmetic theory of adjoint plane curves. Trans. AMS72, 414\u2013436 (1952)","journal-title":"Trans. AMS"},{"key":"BF01195534_CR6","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/BF01398398","volume":"72","author":"L. Gruson","year":"1983","unstructured":"Gruson, L., Lazarsfeld, R., Peskine, C.: On a theorem of Castelnuovo, and the equations defining space curves. Invent. Math.72, 491\u2013506 (1983)","journal-title":"Invent. Math."},{"key":"BF01195534_CR7","volume-title":"Curves in Projective Space","author":"J. Harris","year":"1982","unstructured":"Harris, J.: Curves in Projective Space. Presses Univ. Montr\u00e9al 1982"},{"key":"BF01195534_CR8","doi-asserted-by":"crossref","first-page":"497","DOI":"10.2307\/2372986","volume":"84","author":"R. Hartshorne","year":"1962","unstructured":"Hartshorne, R.: Complete intersections and connectedness. Am. J. Math.84, 497\u2013508 (1962)","journal-title":"Am. J. Math."},{"key":"BF01195534_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3849-0","volume-title":"Algebraic Geometry","author":"R. Hartshorne","year":"1977","unstructured":"Hartshorne, R.: Algebraic Geometry. Berlin, Heidelberg, New York; Springer 1977"},{"key":"BF01195534_CR10","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1215\/kjm\/1250777055","volume":"30","author":"H. Hironaka","year":"1957","unstructured":"Hironaka, H.: On the arithmetic genera and the effective genera of algebraic curves. Mem. Coll. Sci. Univ. Kyoto (A)30, 177\u2013195 (1957)","journal-title":"Mem. Coll. Sci. Univ. Kyoto (A)"},{"key":"BF01195534_CR11","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/0022-314X(91)90023-5","volume":"38","author":"C. Hooley","year":"1991","unstructured":"Hooley, C.: On the number of points on a complete intersection over a finite field. J. Number Theory38, 338\u2013358 (1991)","journal-title":"J. Number Theory"},{"key":"BF01195534_CR12","first-page":"1","volume":"19","author":"J.-R. Joly","year":"1973","unstructured":"Joly, J.-R.: \u00c9quations et vari\u00e9t\u00e9s alg\u00e9briques sur un corps fini. L'Enseign. Math.19, 1\u2013117 (1973)","journal-title":"L'Enseign. Math."},{"key":"BF01195534_CR13","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1093\/qmath\/12.1.217","volume":"12","author":"D. Kirby","year":"1961","unstructured":"Kirby, D.: The genus of an algebraic curve. Quart. J. Math. Oxford (2),12, 217\u2013226 (1961)","journal-title":"Quart. J. Math. Oxford (2)"},{"key":"BF01195534_CR14","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1090\/pspum\/046.2\/927987","volume":"46","author":"S. L. Kleiman","year":"1987","unstructured":"Kleiman, S. L.: Intersection theory and enumerative geometry: a decade in review. Proc. Symp. Pure Math.46, 321\u2013370 (1987)","journal-title":"Proc. Symp. Pure Math."},{"key":"BF01195534_CR15","volume-title":"Introduction to Commutative Algebra and Algebraic Geometry","author":"E. Kunz","year":"1985","unstructured":"Kunz, E.: Introduction to Commutative Algebra and Algebraic Geometry. Basel: Birkh\u00e4user 1985"},{"key":"BF01195534_CR16","doi-asserted-by":"crossref","unstructured":"Leep, D. B., Yeomans, C. C.: The number of points on a singular curve over a finite field, manuscript 1994","DOI":"10.1007\/BF01196671"},{"key":"BF01195534_CR17","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Cambridge Univ. Press 1983"},{"key":"BF01195534_CR18","volume-title":"Algebraic Geometry I: Complex Projective Varieties","author":"D. Mumford","year":"1976","unstructured":"Mumford, D.: Algebraic Geometry I: Complex Projective Varieties. Berlin, Heidelberg, New York: Springer 1976"},{"key":"BF01195534_CR19","volume-title":"Seminar on Deformations. Lecture Notes in Math. Vol. 1165","author":"C. Okonek","year":"1985","unstructured":"Okonek, C., Spindler, H.: Das Spektrum torsionsfreier Garben II. In: J. \u0141awrynowicz (ed.) Seminar on Deformations. Lecture Notes in Math. Vol. 1165. Berlin, Heidelberg, New York: Springer 1985"},{"key":"BF01195534_CR20","doi-asserted-by":"crossref","first-page":"169","DOI":"10.2307\/1969773","volume":"56","author":"M. Rosenlicht","year":"1952","unstructured":"Rosenlicht, M.: Equivalence relations on algebraic curves. Ann. Math. (2)56, 169\u2013191 (1952)","journal-title":"Ann. Math. (2)"},{"key":"BF01195534_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0080437","volume-title":"Equations over Finite Fields: An Elemenatry Approach","author":"W. Schmidt","year":"1976","unstructured":"Schmidt, W.: Equations over Finite Fields: An Elemenatry Approach. [Lecture Notes in Math. Vol. 536] Berlin, Heidelberg, New York: Springer 1976"},{"key":"BF01195534_CR22","unstructured":"Semple, J. G., Roth, L.: Introduction to Algebraic Geometry. Oxford University Press 1985"},{"key":"BF01195534_CR23","first-page":"397","volume":"296","author":"J.-P. Serre","year":"1983","unstructured":"Serre, J.-P.: Sur le nombre des points rationnels d'une courbe alg\u00e9brique sur un corps fini. C. R. Acad. Sci. Paris296, 397\u2013402 (1983)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"BF01195534_CR24","volume-title":"Number Theory: New York Seminar 1989\u20131990","author":"A. T. Vasquez","year":"1991","unstructured":"Vasquez, A. T.: Rational desingularization of a curve defined over a finite field. In: Chudnovsky, D. V. et al. (eds.). Number Theory: New York Seminar 1989\u20131990 Berlin, Heidelberg, New York: Springer 1991"},{"key":"BF01195534_CR25","doi-asserted-by":"crossref","unstructured":"Veronese, G.: de Behandlung der projectivischen Verh\u00e4ltnisse der R\u00e4ume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens. Math. Ann.19 (1882)","DOI":"10.1007\/BF01446461"},{"key":"BF01195534_CR26","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/BF01083190","volume":"17","author":"S. G. Vl\u00e8duts","year":"1983","unstructured":"Vl\u00e8duts, S. G., Drinfel'd, V. G.: The number of points of an algebraic curve. Funktional. Anal, i Prilozhen17, 68\u201369 (1983). [In Russian; English translation in Funct. Anal. Appls.17, 53\u201354 (1883)]","journal-title":"Funktional. Anal, i Prilozhen"},{"key":"BF01195534_CR27","unstructured":"van der Waerden, B. L.: Modern Algebra. 3rd edn., Vol. II. Ungar 1950"},{"key":"BF01195534_CR28","unstructured":"Weil, A.: Sur les Courbes Alg\u00e9briques et les Vari\u00e9t\u00e9s qui s'en D\u00e9duisent. Hermann 1948"},{"key":"BF01195534_CR29","doi-asserted-by":"crossref","first-page":"2055","DOI":"10.1080\/00927878908823835","volume":"17","author":"J. Wolfmann","year":"1989","unstructured":"Wolfmann, J.: The number of points on certain algebraic curves over finite fields. Comm. Algebra17, 2055\u20132060 (1989)","journal-title":"Comm. Algebra"},{"key":"BF01195534_CR30","unstructured":"Zariski, O., Samuel, P.: Commutative Algebra. Vol. I. Van Nostrand 1958"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01195534.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01195534\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01195534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,5]],"date-time":"2020-04-05T20:52:15Z","timestamp":1586119935000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01195534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["BF01195534"],"URL":"https:\/\/doi.org\/10.1007\/bf01195534","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}