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Algebraic de Rham cohomology with torus coefficients

Let $X$ be a smooth projective variety over $\mathbb{C}.$ On page 3 in this preprint of Simpson, it is stated that Notice first of all that the algebraic de Rham theory is not going to work well in ...
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Monodromy group action on de Rham cohomology

Let $f : Y \longrightarrow X := \mathbb{P}^1\setminus\{0,1,\infty\}$ be the smooth proper morphism associated to the Legendre family, which is an elliptic fibration of the punctured line, with fibre ...
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