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Michael Hardy
Michael Hardy
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Suslin Rigidity conjecture states that motivic cohomology $$ H_{\mathcal{M}}^1(Spec(F),\mathbb{Q}(n)) $$$$ H_{\mathcal{M}}^1(\operatorname{Spec}(F),\mathbb{Q}(n)) $$ of the field $F$ coincides with motivic cohomology for the subfield of constants $F_0$.

The fact that first motivic cohomology don’t change under pure transcendental extensions gives some evidence this conjecture.

Question: Does there exist a more conceptual reason for validity of this conjecture? Does it tell us something new about algebraic cycles (under assumption that Standard Conjectures hold)?

Suslin Rigidity conjecture states that motivic cohomology $$ H_{\mathcal{M}}^1(Spec(F),\mathbb{Q}(n)) $$ of the field $F$ coincides with motivic cohomology for the subfield of constants $F_0$.

The fact that first motivic cohomology don’t change under pure transcendental extensions gives some evidence this conjecture.

Question: Does there exist a more conceptual reason for validity of this conjecture? Does it tell us something new about algebraic cycles (under assumption that Standard Conjectures hold)?

Suslin Rigidity conjecture states that motivic cohomology $$ H_{\mathcal{M}}^1(\operatorname{Spec}(F),\mathbb{Q}(n)) $$ of the field $F$ coincides with motivic cohomology for the subfield of constants $F_0$.

The fact that first motivic cohomology don’t change under pure transcendental extensions gives some evidence this conjecture.

Question: Does there exist a more conceptual reason for validity of this conjecture? Does it tell us something new about algebraic cycles (under assumption that Standard Conjectures hold)?

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Daniil Rudenko
Daniil Rudenko
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Motivation for Suslin’s Rigidity Conjecture

Suslin Rigidity conjecture states that motivic cohomology $$ H_{\mathcal{M}}^1(Spec(F),\mathbb{Q}(n)) $$ of the field $F$ coincides with motivic cohomology for the subfield of constants $F_0$.

The fact that first motivic cohomology don’t change under pure transcendental extensions gives some evidence this conjecture.

Question: Does there exist a more conceptual reason for validity of this conjecture? Does it tell us something new about algebraic cycles (under assumption that Standard Conjectures hold)?