1. Drinfeld's Lemma for F-isocrystals, I.
- Author
-
Kedlaya, Kiran S
- Subjects
- *
PRODUCT attributes , *FUNDAMENTAL groups (Mathematics) - Abstract
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 |$\overline{{\mathbb{Q}}}_{\ell }$| -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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF