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Let $X$ be a scheme, and let $D^{*}(X)$ be the unbounded (resp. unbounded, resp. bounded below/above, etc) derived category of coherent sheaves on $X$. The work of Robalo establishes a universal ...

It is well known that the derived category of coherent sheaves (unbounded, bounded, and all cousins) on a scheme $X$ contain most - if not all (depending on specifics) - of the cohomological ...

I am currently reading Künneth spectral sequence, which is given below. Let $R$ be a ring and A$=\big\{A_n,d_n:A_n\longrightarrow A_{n-1}\big|d_{n-1}\circ d_n=0\big\}_{n\in \Bbb Z}$ be a chain ...

There are a few well known constructions of potential categories of pure motives for smooth projective varieties over a field. My understanding is that modulo the standard conjectures these should be ...