Motivic fundamental groups and integral points

@article{Hadian2011MotivicFG,
  title={Motivic fundamental groups and integral points},
  author={Majid Hadian},
  journal={Duke Mathematical Journal},
  year={2011},
  volume={160},
  pages={503-565}
}
  • Majid Hadian
  • Published 1 December 2011
  • Mathematics
  • Duke Mathematical Journal
Computation of the unipotent Albanese map on elliptic and hyperelliptic curves
  • J. Beacom
  • Mathematics
    Annales mathématiques du Québec
  • 2019
We study the unipotent Albanese map appearing in the non-abelian Chabauty method of Minhyong Kim. In particular we explore the explicit computation of the p-adic de Rham period map $$j^{dr}_n$$ j
Chapter 5 The Motivic Logarithm for Curves
The paper explains how in Kim’s approach to diophantine equations étale cohomology can be replaced by motivic cohomology. For this Beilinson’s construction of the motivic logarithm suffices, and it
The Motivic Logarithm for Curves
The paper explains how in Kim’s approach to diophantine equations etale cohomology can be replaced by motivic cohomology. For this Beilinson’s construction of the motivic logarithm suffices, and it
p-adic integrals and linearly dependent points on families of curves I
We prove that the set of ‘low rank’ points on sufficiently large fibre powers of families of curves are not Zariski dense. The recent work of Dimitrov–Gao–Habegger and Kühne (and Yuan) imply the
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The theory of motives concerns the enrichment of (co)homology groups of varieties with extra structure, i.e., the structure of a motive. The problem of similarly enriching the topological fundamental
Local constancy of pro-unipotent Kummer maps
It is a theorem of Kim–Tamagawa that the Q`-pro-unipotent Kummer map associated to a smooth projective curve Y over a finite extension of Qp is locally constant when ` 6= p. The present paper
p-adic iterated integration on semistable curves
We reformulate the theory of p-adic iterated integrals on semistable curves using the unipotent log rigid fundamental group. This fundamental group carries Frobenius and monodromy operators whose
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In [Kim05], Kim gave a new proof of Siegel’s Theorem that there are only finitely many S-integral points on PZ \ {0, 1,∞}. One advantage of Kim’s method is that it in principle allows one to actually
Explicit Motivic Mixed Elliptic Chabauty-Kim
The main point of the paper is to take the explicit motivic Chabauty-Kim method developed in papers of Dan-Cohen–Wewers and Dan-Cohen and the author and make it work for non-rational curves. In
Functional transcendence for the unipotent Albanese map
We prove a certain transcendence property of the unipotent Albanese map of a smooth variety, conditional on the Ax-Schanuel conjecture for variations of mixed Hodge structure. We show that this
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References

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Crystalline cohomology and p-adic Galois-representations
Mathematics around Kim's new proof of Siegel's theorem
The motivic fundamental group of P1∖{0,1,∞} and the theorem of Siegel
In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. In particular, we
Catégories Tannaliennes
  • The Grothendieck Festschrift, Vol. II. Progr. Math.,
  • 1990
Le corps des périodes p-adiques
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Groupes fondamentaux motiviques de Tate mixte
Le Groupe Fondamental de la Droite Projective Moins Trois Points
Le present article doit beaucoup a A. Grothendieck. Il a invente la philosophie des motifs, qui est notre fil directeur. Il y a quelques cinq ans, il m’a aussi dit, avec force, que le complete
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