论文标题
德林菲尔德的引理，用于$ f $ -isocrystals，我
Drinfeld's lemma for $F$-isocrystals, I
论文作者
论文摘要
我们证明，在收敛或过度会议的设置中，在两个或多个平滑方案的绝对产品上，绝对不可还原的$ f $ iSocrystal在特征性$ p $的完美领域的绝对产品上，进一步配备了部分frobenius maps的动作，是$ f $ iSocrystals的外部产品。 Lisse $ \ bar {\ Mathbb {q}} _ \ ell $ -sheaves的相应语句，对于$ \ ell \ neq p $ a Prime，是Drinfeld在特征性$ P $中基本产品基本产物基本产物基本产物基本产物基本群体的结果。后者在V. Lafforgue在V. Langlands的方法中起着关键作用，该兰兰人对具有$ \ ell $ - adiC系数的还原群体的往来； $ p $ - adic类似物将在随后与Daxin Xu的合作中考虑。
We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the partial Frobenius maps, is an external product of $F$-isocrystals over the multiplicands. The corresponding statement for lisse $\bar{\mathbb{Q}}_\ell$-sheaves, for $\ell \neq p$ a prime, is a consequence of Drinfeld's lemma on the fundamental groups of absolute products of schemes in characteristic $p$. The latter plays a key role in V. Lafforgue's approach to the Langlands correspondence for reductive groups with $\ell$-adic coefficients; the $p$-adic analogue will be considered in subsequent work with Daxin Xu.
