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3 votes
0 answers
390 views

Status of motives in higher category theory: motives and algebraic cycles through a higher categorical perspective

A while ago this interesting question was asked Derived Algebraic Geometry and Chow Rings/Chow Motives. Primary question: Have there been any recent developments/advances on the above question? If not,...
Luqman Waheeduddin's user avatar
4 votes
0 answers
539 views

Why do motivic stacks make sense?

In the paper "Motivic model categories and motivic derived algebraic geometry", Yuki Kato, whose email-address I sadly couldn't find out, describes a procedure to "motivy" the objects of any $(\infty,...
Alexander Praehauser's user avatar
4 votes
0 answers
248 views

Derived equivalent varieties with differing integral Mukai-Hodge structures?

For a smooth projective complex variety $X$ of dimension $n$, let $H^i(X)$ denote its integral Hodge structure of weight $i$. Define $\tilde{ H^0}(X) = \bigoplus H^{2i}(X)\otimes \Bbb Z(i)$ and $\...
Dominik's user avatar
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