We show that algebraic de Rham cohomology sheaves of smooth non-Archimedean analytic spaces have canonical decomposition via weights. This in particular confirms a question raised by Berkovich about 1-forms. On the other hand, we study tropical Dolbeault cohomology in the sense of Chambert-Loir and Ducros, and will show a connection between these two theories. Some applications and conjectures will be discussed.

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