Rational motivic path spacesand Kim’s relative unipotent section conjecture

Ishai Dan-Cohen; Tomer Schlank

doi:https://doi.org/10.4171/RSMUP/97

Rational motivic path spacesand Kim’s relative unipotent section conjecture

Ishai Dan-Cohen, Tomer Schlank

Ben-Gurion University of the Negev, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga’s.” Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim’s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.

Original language	American English
Pages (from-to)	117-172
Number of pages	56
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	148
DOIs	https://doi.org/10.4171/RSMUP/97
State	Published - 1 Jan 2022

Keywords

Rational homotopy
motivic homotopy
nonabelian Chabauty
rational points
unipotent fundamental group

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Mathematical Physics
Geometry and Topology

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title = "Rational motivic path spacesand Kim{\textquoteright}s relative unipotent section conjecture",

abstract = "We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga{\textquoteright}s.” Works of White and Cisinski and D{\'e}glise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim{\textquoteright}s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.",

keywords = "Rational homotopy, motivic homotopy, nonabelian Chabauty, rational points, unipotent fundamental group",

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AU - Schlank, Tomer

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N2 - We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga’s.” Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim’s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.

AB - We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga’s.” Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim’s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.

KW - Rational homotopy

KW - motivic homotopy

KW - nonabelian Chabauty

KW - rational points

KW - unipotent fundamental group

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EP - 172

JO - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

JF - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

ER -

Rational motivic path spacesand Kim’s relative unipotent section conjecture

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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