اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBlochs cycle complex of zero cycles with $mathbb Z/p^n$ coefficients from Grothendiecks coherent duality point of view
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تأليف
Fei Ren
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Let $X$ be a separated scheme of finite type over $k$ with $k$ being a perfect field of positive characteristic $p$. In this work we define a complex $K_{n,X,log}$ via Grothendiecks duality theory of coherent sheaves following Kato and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves $tilde u_{n,X}$ to $K_{n,X,log}$ for the etale topology, and also for the Zariski topology under the extra assumption $k=bar k$. Combined with Zhongs quasi-isomorphism from Blochs cycle complex $mathbb Z^c_{X}$ to $tilde u_{n,X}$, we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of $0$-cycles with $mathbb Z/p^n$-coefficients.
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