Reciprocity sheaves and abelian ramification theory.
Reciprocity sheaves and abelian ramification theory.
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互易滑轮和阿贝尔分枝理论。
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
S. Saito
中科院分区：
文献类型：
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作者：
Kay Rülling;S. Saito
我们定义了一个motivic导体的任何预层转移$F$使用的范畴框架理论的动机与模量的卡恩斋藤山崎。如果$F$是一个互易层，这个导体在$F（L）$上产生一个递增的和穷举的过滤，其中$L$是完美基域上的任何几何型的亨塞尔离散赋值域。证明了若F是一个光滑群概型，则运动导体是Rosenlicht-Serre导体的推广，若F赋X为交换化的E基本群上的有限特征标群，则运动导体与Kato-Matsuda定义的Artin导体一致;如果$F$赋予$X$可积秩为1的联络群（特征为零），则它与不规则性一致。我们还表明，这台机器产生了一个导体的torsors有限平坦群计划的基础领域，我们相信这是新的。我们引入了带转移的预层上导体的一般概念，并证明了在互易层上运动导体是最小的，并且任何只定义在具有{em完美}剩余域的几何型hensel离散赋值域上的导体都可以唯一地推广到所有这样的域上，而对剩余域没有任何限制.例如Kato-Matsuda Artin导体被刻画为经典Artin导体在完美剩余域情形下的正则扩张。
We define a motivic conductor for any presheaf with transfers $F$ using the categorical framework developed for the theory of motives with modulus by Kahn-Saito-Yamazaki. If $F$ is a reciprocity sheaf this conductor yields an increasing and exhaustive filtration on $F(L)$, where $L$ is any henselian discrete valuation field of geometric type over the perfect ground field. We show if $F$ is a smooth group scheme, then the motivic conductor extends the Rosenlicht-Serre conductor; if $F$ assigns to $X$ the group of finite characters on the abelianized 'etale fundamental group of $X$, then the motivic conductor agrees with the Artin conductor defined by Kato-Matsuda; if $F$ assigns to $X$ the group of integrable rank one connections (in characteristic zero), then it agrees with the irregularity. We also show that this machinery gives rise to a conductor for torsors under finite flat group schemes over the base field, which we believe to be new. We introduce a general notion of conductors on presheaves with transfers and show that on a reciprocity sheaf the motivic conductor is minimal and any conductor which is defined only for henselian discrete valuation fields of geometric type with {em perfect} residue field can be uniquely extended to all such fields without any restriction on the residue field. For example the Kato-Matsuda Artin conductor is characterized as the canonical extension of the classical Artin conductor defined in the perfect residue field case.
具有模数和高维类场论的 $0$ 循环 Chow 群
影响因子：
2.5
作者：
Moritz Kerz;Shuji Saito
通讯作者：
Shuji Saito