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.
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Treatment of emerging contaminants in simulated wastewater via tandem photo-Fenton-like reaction and nutrient recovery
Nutrient rich wastewater containing emerging organic contaminants was used for struvite synthesis with a novel tandem process with a heterogeneous Fenton oxidation pretreatment.
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- Award ID(s):
- 1710120
- PAR ID:
- 10478263
- Publisher / Repository:
- RSC
- Date Published:
- Journal Name:
- Environmental Science: Water Research & Technology
- Volume:
- 9
- Issue:
- 2
- ISSN:
- 2053-1400
- Page Range / eLocation ID:
- 508 to 522
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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