The Brown-Comenetz dual of the K(2)-local sphere at the prime 3

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• 作者：Paul G. Goerss^a ; ^{pgoerss@math.northwestern.edu" class="auth_mail" title="E-mail the corresponding author} ; Hans-Werner Henn^b ; ^{henn@math.unistra.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Chromatic stable homotopy theory ; Brown&ndash ; Comenetz duality
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：22 January 2016
• 年：2016
• 卷：288
• 期：Complete
• 页码：648-678
• 全文大小：572 K

文摘

We calculate the homotopy type of the Brown–Comenetz dual class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815003321&_mathId=si1.gif&_user=111111111&_pii=S0001870815003321&_rdoc=1&_issn=00018708&md5=03691fae943c324cf9d5db3cc3464ad0" title="Click to view the MathML source">I₂class="mathContainer hidden">class="mathCode">$I_2$ of the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815003321&_mathId=si2.gif&_user=111111111&_pii=S0001870815003321&_rdoc=1&_issn=00018708&md5=9baa6cec324f717cc951f2ed373687d6" title="Click to view the MathML source">K(2)class="mathContainer hidden">class="mathCode">$K(2)$-local sphere at the prime 3 and show that there is an equivalence in the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815003321&_mathId=si2.gif&_user=111111111&_pii=S0001870815003321&_rdoc=1&_issn=00018708&md5=9baa6cec324f717cc951f2ed373687d6" title="Click to view the MathML source">K(2)class="mathContainer hidden">class="mathCode">$K(2)$-local category between class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815003321&_mathId=si1.gif&_user=111111111&_pii=S0001870815003321&_rdoc=1&_issn=00018708&md5=03691fae943c324cf9d5db3cc3464ad0" title="Click to view the MathML source">I₂class="mathContainer hidden">class="mathCode">$I_2$ and a smash product of the determinant twisted sphere and an exotic element P in the Picard group. We give a characterization of P   as well. A secondary aim of the paper is to extend our library of calculations in the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815003321&_mathId=si2.gif&_user=111111111&_pii=S0001870815003321&_rdoc=1&_issn=00018708&md5=9baa6cec324f717cc951f2ed373687d6" title="Click to view the MathML source">K(2)class="mathContainer hidden">class="mathCode">$K(2)$-local category.