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Drinfeld's Lemma for F-isocrystals, I.
- Source :
-
IMRN: International Mathematics Research Notices . Jun2024, Vol. 2024 Issue 11, p9340-9358. 19p. - Publication Year :
- 2024
-
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]
- Subjects :
- *PRODUCT attributes
*FUNDAMENTAL groups (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2024
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 177947389
- Full Text :
- https://doi.org/10.1093/imrn/rnae039