The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold

Pridham, J. P.

doi:10.5802/afst.1143

Cited by 14 publications

(24 citation statements)

References 9 publications

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“…The proof now proceeds as in [Pri2] Proposition 6.7. cannot be the geometric fundamental group of any smooth proper variety defined over the algebraic closure of a finite field.…”

Section: If X Is Merely Smooth Andmentioning

confidence: 93%

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Weight decompositions on étale fundamental groups

Pridham¹

2009

ajm

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“…The proof now proceeds as in [Pri2] Proposition 6.7. cannot be the geometric fundamental group of any smooth proper variety defined over the algebraic closure of a finite field.…”

Section: If X Is Merely Smooth Andmentioning

confidence: 93%

“…The group R u ( W ̟ 1 (X,x)) is the universal deformation ρ : π 1 (X,x) → U ⋊ for U pro-unipotent. In [Pri2], a theory of deformations over nilpotent Lie algebras with G-actions was developed, and this enables us to analyse our scenario.…”

Section: Introductionmentioning

confidence: 99%

Weight decompositions on étale fundamental groups

Pridham¹

2009

ajm

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“…where exp(H 0 (Y, adB ρ )) ⊂ exp(g) acts on (Z, 0) via the adjoint action. We now proceed as in [Pri3,Remarks 6.6]. Given a real Artinian local ring A = R⊕m(A), observe that G(A) × G(R) R(R) ∼ = exp(g ⊗ m(A)) ⋊ R(R).…”

Section: Strictificationmentioning

confidence: 99%

Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting

Pridham

2016

Memoirs of the AMS

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We define and construct mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x − i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.

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“…where R u (G) is the pro-unipotent radical of G, and G red = G/R u (G) is pro-reductive (see [26] for details). Representations of G red are in one to one correspondence with semi-simple representations of G via the pullback by the projection G → G red .…”

Section: Notations and Terminologiesmentioning

confidence: 99%

The de Rham homotopy theory and differential graded category

Moriya

2011

Math. Z.

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This paper is a generalization of [30]. We develop the de Rham homotopy theory of not necessarily nilpotent spaces. We use two algebraic objects: closed dg-categories and equivariant dg-algebras. We see these two objects correspond in a certain way (Prop.3.3.4, Thm.3.4.5). We prove an equivalence between the homotopy category of schematic homotopy types [22] and a homotopy category of closed dg-categories (Thm.1.0.1). We give a description of homotopy invariants of spaces in terms of minimal models (Thm.1.0.2). The minimal model in this context behaves much like the Sullivan's minimal model. We also provide some examples. We prove an equivalence between fiberwise rationalizations [5] and closed dg-categories with subsidiary data (Thm.1.0.4).

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The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold

Cited by 14 publications

References 9 publications

Weight decompositions on étale fundamental groups

Weight decompositions on étale fundamental groups

Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting

The de Rham homotopy theory and differential graded category

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