{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:37:11Z","timestamp":1776800231811,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"299","license":[{"start":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T00:00:00Z","timestamp":1470873600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 10871106"],"award-info":[{"award-number":["No. 10871106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we prove that the tame kernel of the cyclotomic field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q left-parenthesis zeta 5 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b6\n                                \n                              <\/mml:mi>\n                              <mml:mn>5<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(\\zeta _5)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is trivial, which confirms a conjecture of Browkin.\n                  <\/p>","DOI":"10.1090\/mcom\/3003","type":"journal-article","created":{"date-parts":[[2015,8,11]],"date-time":"2015-08-11T10:54:21Z","timestamp":1439290461000},"page":"1523-1538","source":"Crossref","is-referenced-by-count":3,"title":["The tame kernel of \u211a(\ud835\udf01\u2085) is trivial"],"prefix":"10.1090","volume":"85","author":[{"given":"Long","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kejian","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,8,11]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"534","DOI":"10.2307\/1970769","article-title":"A finiteness theorem for \ud835\udc3e\u2082 of a number field","volume":"94","author":"Garland, Howard","year":"1971","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/BFb0073733","article-title":"The Milnor ring of a global field","author":"Bass, H.","year":"1973"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1023\/B:KTHE.0000028979.91416.00","article-title":"Generators and relations for \ud835\udc3e\u2082\ud835\udcaa_{\u2131}","volume":"31","author":"Belabas, Karim","year":"2004","journal-title":"$K$-Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0920-3036","issn-type":"print"},{"key":"4","isbn-type":"print","first-page":"187","article-title":"The functor \ud835\udc3e\u2082 for the ring of integers of a number field","author":"Browkin, Jerzy","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/8301021454"},{"issue":"225","key":"5","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1090\/S0025-5718-99-01000-5","article-title":"Tame and wild kernels of quadratic imaginary number fields","volume":"68","author":"Browkin, Jerzy","year":"1999","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"232","key":"6","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1090\/S0025-5718-00-01182-0","article-title":"Computing the tame kernel of quadratic imaginary fields","volume":"69","author":"Browkin, Jerzy","year":"2000","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"7","unstructured":"J. Browkin, Construction of elements in Bloch group, preprint."},{"issue":"5","key":"8","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/BF00535049","article-title":"On the structure of the \ud835\udc3e\u2082 of the ring of integers in a number field","volume":"2","author":"Keune, Frans","year":"1989","journal-title":"$K$-Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0920-3036","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0022-4049(94)90124-4","article-title":"Computation of \ud835\udc3e\u2082\ud835\udc19[\u221a-6]","volume":"96","author":"Qin, Hou Rong","year":"1994","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"issue":"1","key":"10","first-page":"63","article-title":"Computation of \ud835\udc3e\u2082\ud835\udc4d[(1+\u221a-35)\/2]","volume":"17","author":"Qin, Hourong","year":"1996","journal-title":"Chinese Ann. Math. Ser. B","ISSN":"https:\/\/id.crossref.org\/issn\/0252-9599","issn-type":"print"},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1006\/jnth.1994.1016","article-title":"Generalization of Thue\u2019s theorem and computation of the group \ud835\udc3e\u2082\ud835\udc42_{\ud835\udc39}","volume":"46","author":"Ska\u0142ba, Mariusz","year":"1994","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"12","first-page":"524","article-title":"Letter from Tate to Iwasawa on a relation between \ud835\udc3e\u2082 and Galois cohomology","author":"Tate, J.","year":"1973"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1081\/AGB-120017338","article-title":"Computing the tame kernel of \u211a(\ud835\udf01\u2088)","volume":"31","author":"Guo, Xuejun","year":"2003","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-299\/S0025-5718-2015-03003-8\/S0025-5718-2015-03003-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-299\/S0025-5718-2015-03003-8\/S0025-5718-2015-03003-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:45:52Z","timestamp":1776797152000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-299\/S0025-5718-2015-03003-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,11]]},"references-count":13,"journal-issue":{"issue":"299","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["S0025-5718-2015-03003-8"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3003","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":[[2015,8,11]]}}}