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Suppose that: $X$ is a smooth complex algebraic variety, $f : X \to D$ is a proper map to a small disc, smooth away from 0, $Z_\epsilon = f^{-1}(\epsilon)$, and $Z = Z_0$. Then there is a procedure (...

I am studying certain weights for (triangulated categories of relative) motives. Those are interesting; yet one can hardly say that they are very much explicit or effectively computable. So, I would ...

In Weil II, Deligne proves that the six functors preserve the category of mixed $l$-adic complexes. Most difficulties are encountered when proving that if $f\colon X\to Y$ is a finite type separated ...