{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:48:30Z","timestamp":1776721710636,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"213","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    For\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"r equals 7\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>7<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">r=7<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and 8 we consider an action of the Weyl group of type\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper E Subscript r\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>E<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mspace width=\"thinmathspace\"\/>\n                              <mml:mi>r<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">E_{\\,r}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    on a unimodular lattice of rank\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"r plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">r+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We give the tables of the first cohomology groups for all cyclic subgroups of the Weyl group with respect to this action. These are important in the arithmetic theory of Del Pezzo surfaces.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00681-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"247-258","source":"Crossref","is-referenced-by-count":9,"title":["Calculation of Manin\u2019s invariant for Del Pezzo surfaces"],"prefix":"10.1090","volume":"65","author":[{"given":"Tohsuke","family":"Urabe","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","unstructured":"N. Bourbaki, Groupes et alg\u00e8bre de Lie, Chaps. 4\u20136, Hermann, Paris, 1968."},{"key":"2","doi-asserted-by":"publisher","first-page":"23","DOI":"10.2307\/1989990","article-title":"Steinitz field towers for modular fields","volume":"46","author":"MacLane, Saunders","year":"1939","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"3","doi-asserted-by":"crossref","unstructured":"E. Cartan, Sur la r\u00e9duction \u00e0 sa forme canonique de la structure d\u2019un groupe de transformations fini et continu, Amer. J. Math. 18 (1896), 1\u201361.","DOI":"10.2307\/2369787"},{"key":"4","first-page":"1","article-title":"Conjugacy classes in the Weyl group","volume":"25","author":"Carter, R. W.","year":"1972","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"key":"5","doi-asserted-by":"crossref","unstructured":"H. S. M. Coxeter, Finite groups generated by reflections and their subgroups generated by reflections, Proc. Cambridge Philos. Soc. 30 (1934), 466\u2013482.","DOI":"10.1017\/S0305004100012718"},{"key":"6","doi-asserted-by":"crossref","unstructured":"Patric Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction, (Part II), Proc. Cambridge Philos. Soc. 30 (1934), 460\u2013465.","DOI":"10.1017\/S0305004100012706"},{"key":"7","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"key":"8","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"37","key":"9","first-page":"113","article-title":"del Pezzo surfaces of degree four","author":"Kunyavski\u012d, B. \u00c8.","year":"1989","journal-title":"M\\'{e}m. Soc. Math. France (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/0037-9484","issn-type":"print"},{"issue":"30","key":"10","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF02684356","article-title":"Rational surfaces over perfect fields","author":"Manin, Ju. I.","year":"1966","journal-title":"Inst. Hautes \\'{E}tudes Sci. Publ. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0073-8301","issn-type":"print"},{"key":"11","series-title":"North-Holland Mathematical Library","isbn-type":"print","volume-title":"Cubic forms","volume":"4","author":"Manin, Yu. I.","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/0444878238","edition":"2"},{"key":"12","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1007\/BF01403184","article-title":"The Brauer group of a rational surface","volume":"11","author":"Milne, J. S.","year":"1970","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"key":"13","series-title":"Princeton Mathematical Series, No. 33","isbn-type":"print","volume-title":"\\'{E}tale cohomology","author":"Milne, James S.","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/0691082383"},{"issue":"3","key":"14","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1017\/S0305004100076106","article-title":"The Brauer group of cubic surfaces","volume":"113","author":"Swinnerton-Dyer, Peter","year":"1993","journal-title":"Math. Proc. Cambridge Philos. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0305-0041","issn-type":"print"},{"key":"15","unstructured":"T. Urabe, maninh1, Mathematica notebooks for calculation of Del Pezzo surfaces of degree 2 or 1, anonymous ftp-able, \/tnt\/maninh1-mac.tar.Z, ftp.math.metro-u.ac.jp (1994)."},{"key":"16","unstructured":"S. Wolfram, Mathematica, A system for doing mathematics by computer, Addison-Wesley, Redwood City, 1988."},{"issue":"2","key":"17","first-page":"211","article-title":"The Brauer group of an abelian variety over a finite field","volume":"46","author":"Zarkhin, Yu. G.","year":"1982","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat.","ISSN":"https:\/\/id.crossref.org\/issn\/0373-2436","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00681-3\/S0025-5718-96-00681-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00681-3\/S0025-5718-96-00681-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:02:10Z","timestamp":1776718930000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00681-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":17,"journal-issue":{"issue":"213","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["S0025-5718-96-00681-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00681-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}