Motives of complex-analytic spacesIs it possible to classify all Weil cohomologies?Coefficients of Weil Cohomology TheoriesWhat is the relationship between motivic cohomology and the theory of motives?Motives and homotopy theories of algebraic varieties$l$-adic periods?Current status of independence of Betti numbers for different Weil cohomology theories
Motives of complex-analytic spaces
Is it possible to classify all Weil cohomologies?Coefficients of Weil Cohomology TheoriesWhat is the relationship between motivic cohomology and the theory of motives?Motives and homotopy theories of algebraic varieties$l$-adic periods?Current status of independence of Betti numbers for different Weil cohomology theories
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In any setting where we have a notion of space and a notion of cohomology theory, we in principle could ask "what are motives in this setting?". In some settings the question can be interesting (i.e. algebraic varieties and Weil cohomology theories), in some settings not so much (i.e. topological spaces and cohomology theories satisfying all of the Eilbenberg--Steenrod axioms).
For complex-analytic spaces, I am not completely sure how should we define a good cohomology theory. First question: what are some ways to define this notion? Presumably rational Betti cohomology and de Rham cohomology should be examples of good cohomology theories. Second: can we study motives in this setting? I would guess that the answer turns out to be boring, but it would be nice if there is a 3-page paper where this is proved.
ag.algebraic-geometry complex-geometry motives
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$begingroup$
In any setting where we have a notion of space and a notion of cohomology theory, we in principle could ask "what are motives in this setting?". In some settings the question can be interesting (i.e. algebraic varieties and Weil cohomology theories), in some settings not so much (i.e. topological spaces and cohomology theories satisfying all of the Eilbenberg--Steenrod axioms).
For complex-analytic spaces, I am not completely sure how should we define a good cohomology theory. First question: what are some ways to define this notion? Presumably rational Betti cohomology and de Rham cohomology should be examples of good cohomology theories. Second: can we study motives in this setting? I would guess that the answer turns out to be boring, but it would be nice if there is a 3-page paper where this is proved.
ag.algebraic-geometry complex-geometry motives
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add a comment
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$begingroup$
In any setting where we have a notion of space and a notion of cohomology theory, we in principle could ask "what are motives in this setting?". In some settings the question can be interesting (i.e. algebraic varieties and Weil cohomology theories), in some settings not so much (i.e. topological spaces and cohomology theories satisfying all of the Eilbenberg--Steenrod axioms).
For complex-analytic spaces, I am not completely sure how should we define a good cohomology theory. First question: what are some ways to define this notion? Presumably rational Betti cohomology and de Rham cohomology should be examples of good cohomology theories. Second: can we study motives in this setting? I would guess that the answer turns out to be boring, but it would be nice if there is a 3-page paper where this is proved.
ag.algebraic-geometry complex-geometry motives
$endgroup$
In any setting where we have a notion of space and a notion of cohomology theory, we in principle could ask "what are motives in this setting?". In some settings the question can be interesting (i.e. algebraic varieties and Weil cohomology theories), in some settings not so much (i.e. topological spaces and cohomology theories satisfying all of the Eilbenberg--Steenrod axioms).
For complex-analytic spaces, I am not completely sure how should we define a good cohomology theory. First question: what are some ways to define this notion? Presumably rational Betti cohomology and de Rham cohomology should be examples of good cohomology theories. Second: can we study motives in this setting? I would guess that the answer turns out to be boring, but it would be nice if there is a 3-page paper where this is proved.
ag.algebraic-geometry complex-geometry motives
ag.algebraic-geometry complex-geometry motives
asked May 6 at 12:22
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See theorem 1.8 of (Joseph Ayoub. Note sur les opérations de Grothendieck et la réalisation de Betti.
J. Inst. Math. Jussieu.)
You can set up a theory of analytic motives, and the resulting category is equivalent to the derived category of vector spaces (over your field of coefficients, typically $mathbbQ$).
In https://arxiv.org/pdf/1810.04968v1.pdf the analogue for p-adic analytic geometry is proven by Bambozzi and Vezzani. (Maybe also relevant: https://arxiv.org/pdf/1708.04284.pdf)
answered May 6 at 13:25
jmcjmc
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$begingroup$
See theorem 1.8 of (Joseph Ayoub. Note sur les opérations de Grothendieck et la réalisation de Betti.
J. Inst. Math. Jussieu.)
You can set up a theory of analytic motives, and the resulting category is equivalent to the derived category of vector spaces (over your field of coefficients, typically $mathbbQ$).
In https://arxiv.org/pdf/1810.04968v1.pdf the analogue for p-adic analytic geometry is proven by Bambozzi and Vezzani. (Maybe also relevant: https://arxiv.org/pdf/1708.04284.pdf)
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
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$begingroup$
See theorem 1.8 of (Joseph Ayoub. Note sur les opérations de Grothendieck et la réalisation de Betti.
J. Inst. Math. Jussieu.)
You can set up a theory of analytic motives, and the resulting category is equivalent to the derived category of vector spaces (over your field of coefficients, typically $mathbbQ$).
In https://arxiv.org/pdf/1810.04968v1.pdf the analogue for p-adic analytic geometry is proven by Bambozzi and Vezzani. (Maybe also relevant: https://arxiv.org/pdf/1708.04284.pdf)
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
$endgroup$
add a comment
|
$begingroup$
See theorem 1.8 of (Joseph Ayoub. Note sur les opérations de Grothendieck et la réalisation de Betti.
J. Inst. Math. Jussieu.)
You can set up a theory of analytic motives, and the resulting category is equivalent to the derived category of vector spaces (over your field of coefficients, typically $mathbbQ$).
In https://arxiv.org/pdf/1810.04968v1.pdf the analogue for p-adic analytic geometry is proven by Bambozzi and Vezzani. (Maybe also relevant: https://arxiv.org/pdf/1708.04284.pdf)
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
$endgroup$
See theorem 1.8 of (Joseph Ayoub. Note sur les opérations de Grothendieck et la réalisation de Betti.
J. Inst. Math. Jussieu.)
You can set up a theory of analytic motives, and the resulting category is equivalent to the derived category of vector spaces (over your field of coefficients, typically $mathbbQ$).
In https://arxiv.org/pdf/1810.04968v1.pdf the analogue for p-adic analytic geometry is proven by Bambozzi and Vezzani. (Maybe also relevant: https://arxiv.org/pdf/1708.04284.pdf)
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
answered May 6 at 13:25
jmcjmc
3,10416 silver badges39 bronze badges
3,10416 silver badges39 bronze badges
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