Bivariance, Grothendieck duality and Hochschild homology, II: The fundamental class of a flat scheme-map

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• 作者：Leovigildo Alonso Tarrí ; o^a ; ^{leo.alonso@usc.es" class="auth_mail} ; ; Ana Jeremí ; as Ló ; pez^a ; ^{ana.jeremias@usc.es" class="auth_mail} ; Joseph Lipman^b ; ^{lipman@math.purdue.edu" class="auth_mail} ;
• 关键词：14F99
• 刊名：Advances in Mathematics
• 出版年：1 June, 2014
• 年：2014
• 卷：257
• 期：Complete
• 页码：365-461
• 全文大小：962 K

文摘

Fix a noetherian scheme S. For any flat map of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map , the fundamental class of f, where is the (pre-)Hochschild complex of an S-scheme Z and is the twisted inverse image coming from Grothendieck duality theory. When and f is essentially smooth of relative dimension n, this gives an isomorphism . We focus mainly on transitivity of vis-脿-vis compositions , and on the compatibility of with flat base change. These properties imply that orients the flat maps in the bivariant theory of part I , compatibly with essentially 茅tale base change. Furthermore, leads to a dual oriented bivariant theory, whose homology is the classical Hochschild homology of flat S-schemes. When , is used to define a duality map , an isomorphism if f is essentially smooth. These results apply in particular to flat essentially-finite-type maps of noetherian rings.