(Higher) extensions of mixed Hodge structuresEichler-Shimura isomorphism and mixed Hodge theoryMixed Hodge...
(Higher) extensions of mixed Hodge structures
Eichler-Shimura isomorphism and mixed Hodge theoryMixed Hodge structure on the rational homotopy typeThe associated graded of a mixed Hodge moduleextensions of mixed Hodge structuresIs there a description of variation of (mixed) Hodge Structures in terms of a Deligne operator?Mixed Hodge structure on sheaf cohomology of a variation of Hodge structuresDoes the “holomorphic spheres-to-continuous spheres” forgetful function respect the mixed Hodge structures on homotopy groups?Is the category of mixed Hodge modules bi-filtered?Comparing Frobenius weights with Mixed Hodge theoryDeligne's Mixed Hodge Theory
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Mixed Hodge structure is introduced by Deligne and it's very useful for studying complex algebraic varieties. We know $text{MHS}$, the category of mixed Hodge structures is an abelian category. Where can I find a good reference for the computation of the (higher) extension groups inside MHS (and it's variations)? Carlson's paper "Extensions of mixed Hodge structures" is helpful, but I hope a more general reference.
For instance, let $text{MHS}^+_{mathbb R}$ denote the category of mixed Hodge structures equipped with an involution $phi_{infty}$ preserving the weight filtration and such that $phi_{infty} otimes c$ preserves the Hodge filtration (here $c$ means complex conjugation). Is there no $operatorname{Ext}^{2}$ in this category?
ag.algebraic-geometry linear-algebra hodge-theory
asked 9 hours ago
sawdadasawdada
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Mixed Hodge structure is introduced by Deligne and it's very useful for studying complex algebraic varieties. We know $text{MHS}$, the category of mixed Hodge structures is an abelian category. Where can I find a good reference for the computation of the (higher) extension groups inside MHS (and it's variations)? Carlson's paper "Extensions of mixed Hodge structures" is helpful, but I hope a more general reference.
For instance, let $text{MHS}^+_{mathbb R}$ denote the category of mixed Hodge structures equipped with an involution $phi_{infty}$ preserving the weight filtration and such that $phi_{infty} otimes c$ preserves the Hodge filtration (here $c$ means complex conjugation). Is there no $operatorname{Ext}^{2}$ in this category?
ag.algebraic-geometry linear-algebra hodge-theory
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
$endgroup$
add a comment |
$begingroup$
Mixed Hodge structure is introduced by Deligne and it's very useful for studying complex algebraic varieties. We know $text{MHS}$, the category of mixed Hodge structures is an abelian category. Where can I find a good reference for the computation of the (higher) extension groups inside MHS (and it's variations)? Carlson's paper "Extensions of mixed Hodge structures" is helpful, but I hope a more general reference.
For instance, let $text{MHS}^+_{mathbb R}$ denote the category of mixed Hodge structures equipped with an involution $phi_{infty}$ preserving the weight filtration and such that $phi_{infty} otimes c$ preserves the Hodge filtration (here $c$ means complex conjugation). Is there no $operatorname{Ext}^{2}$ in this category?
ag.algebraic-geometry linear-algebra hodge-theory
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
$endgroup$
Mixed Hodge structure is introduced by Deligne and it's very useful for studying complex algebraic varieties. We know $text{MHS}$, the category of mixed Hodge structures is an abelian category. Where can I find a good reference for the computation of the (higher) extension groups inside MHS (and it's variations)? Carlson's paper "Extensions of mixed Hodge structures" is helpful, but I hope a more general reference.
For instance, let $text{MHS}^+_{mathbb R}$ denote the category of mixed Hodge structures equipped with an involution $phi_{infty}$ preserving the weight filtration and such that $phi_{infty} otimes c$ preserves the Hodge filtration (here $c$ means complex conjugation). Is there no $operatorname{Ext}^{2}$ in this category?
ag.algebraic-geometry linear-algebra hodge-theory
ag.algebraic-geometry linear-algebra hodge-theory
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
asked 9 hours ago
sawdadasawdada
2,0941 gold badge4 silver badges31 bronze badges
asked 9 hours ago
sawdadasawdada
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1 Answer
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Beilinson, Notes on absolute Hodge cohomology is another reference.
To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $1$, i.e. there is no $Ext^i$ for $i>1$. See 1.10 of Beilinson's paper.
answered 8 hours ago
Donu ArapuraDonu Arapura
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1 Answer
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$begingroup$
Beilinson, Notes on absolute Hodge cohomology is another reference.
To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $1$, i.e. there is no $Ext^i$ for $i>1$. See 1.10 of Beilinson's paper.
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
$endgroup$
add a comment |
$begingroup$
Beilinson, Notes on absolute Hodge cohomology is another reference.
To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $1$, i.e. there is no $Ext^i$ for $i>1$. See 1.10 of Beilinson's paper.
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
$endgroup$
add a comment |
$begingroup$
Beilinson, Notes on absolute Hodge cohomology is another reference.
To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $1$, i.e. there is no $Ext^i$ for $i>1$. See 1.10 of Beilinson's paper.
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
$endgroup$
Beilinson, Notes on absolute Hodge cohomology is another reference.
To answer your last question, the cohomological dimension of the category of mixed Hodge structures is $1$, i.e. there is no $Ext^i$ for $i>1$. See 1.10 of Beilinson's paper.
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
answered 8 hours ago
Donu ArapuraDonu Arapura
26k2 gold badges68 silver badges128 bronze badges
26k2 gold badges68 silver badges128 bronze badges
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