Lefschetz hyperplane theorem, compares the homology/cohomology of a projective variety with a hyperplane section of it and claims they are isomorphic in certain ranges. There are Lefschetz type theorems for picard groups. There is also a such a conjectures for Chow groups. I was wondering whether there are similar theorem/conjectures for algebraic $K$-theory or motivic cohomology with different coefficients?
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$\begingroup$ presumably you already know about infinitesimal lefschetz for k-cohomology? $\endgroup$– Elden ElmantoFeb 11, 2021 at 13:30
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$\begingroup$ I've seen a version of that, deals with Chow groups. $\endgroup$– user127776Feb 11, 2021 at 13:38
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$\begingroup$ yeah it's the only way I (obviously this is a defect on my part) can imagine such a statement holding. The problem is that K-theory is very "noncommutative" but the lefschetz hyperplane theorem is very "commutative"; in particular it is a statement which needs "degree" or "dimension" to formulate. $\endgroup$– Elden ElmantoFeb 11, 2021 at 14:04
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