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Title: Drinfeld’s Lemma for F -isocrystals, I
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.  more » « less
Award ID(s):
2053473
PAR ID:
10511421
Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
International Mathematics Research Notices
ISSN:
1073-7928
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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