-displays and π-divisible formal -modules

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• 作者：Tobias Ahsendorf^a ; ^{tobias.ahsendorf@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Chuangxun Cheng^b ; ^c ; ^{cxcheng@nju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Thomas Zink^c ; ^{zink@math.uni-bielefeld.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：OO-displays ; π   ; -Divisible formal OO-modules ; OO-frames ; OO-windows ; Universal extensions ; Grothendieck&ndash ; Messing crystals
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：457
• 期：Complete
• 页码：129-193
• 全文大小：889 K

文摘

In this paper, we construct an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-display theory and prove that, under certain conditions on the base ring, the category of nilpotent class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-displays and the category of π  -divisible formal class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-modules are equivalent. Starting with this result, we then construct a Dieudonné class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-display theory and prove a similar equivalence between the category of Dieudonné class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-displays and the category of π  -divisible class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316001289&_mathId=si1.gif&_user=111111111&_pii=S0021869316001289&_rdoc=1&_issn=00218693&md5=08126da90405886eaacfc89e1037ab55" title="Click to view the MathML source">Oclass="mathContainer hidden">class="mathCode">$\mathcal{O}$-modules. We also show that this equivalence is compatible with duality. These results generalize the corresponding results of Zink and Lau on displays and p-divisible groups.