11 citations · 22 across the 16 of their papers we have counts for
17 papers
Coarse moduli of motivic augmentations
Ishai Dan-Cohen
A variety over a suitable base gives rise to a highly structured algebra in motives over . In turn, a -point gives rise to an augmentation . Th…
A curve and its abstract generalized Jacobian
Benjamin Castle, Ishai Dan-Cohen, Assaf Hasson
To a smooth proper curve over a field equipped with a -point and an effective divisor coprime to , one may associate the abstract group $J_{\mathfra…
-adic Periods and Selmer Scheme Images
David Corwin, Ishai Dan-Cohen
The Chabauty--Kim method was developed with the aim of approaching effective Faltings', the problem of explicitly determining the finite set of rational points on a hyperbolic curv…
A motivic Weil height machine for curves
L. Alexander Betts, Ishai Dan-Cohen
The rational points of a smooth curve over a number field map to the set of augmentations of the associated motivic algebra. An expectation, related to Kim's conjecture, is…
On André periods of mixed Tate motives
Ishai Dan-Cohen
In this note, we show that the -adic periods of motives introduced recently by Ancona and Frăţilă (``André periods'') reduce to the classically studied notion in the case of Mix…
Relative tensor products and Koszul duality in monoidal oo-categories
Ishai Dan-Cohen, Asaf Horev
This semi-expository work covers central aspects of the theory of relative tensor products as developed in Higher Algebra, as well as their application to Koszul duality for algebr…
: Towards the Chabauty-Kim method in higher dimensions
Ishai Dan-Cohen, David Jarossay
If Z is an open subscheme of Spec ZZ, X is a sufficiently nice Z-model of a smooth curve over QQ, and p is a closed point of Z, the Chabauty-Kim method leads to the construction of…
The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory I
David Corwin, Ishai Dan-Cohen
Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic q…
The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory II
Ishai Dan-Cohen, David Corwin
Building on work by Dan-Cohen--Wewers, Dan-Cohen [DC], and Brown, we push the computational boundary of our explicit motivic version of Kim's method in the case of the thrice punct…
Morphisms of rational motivic homotopy types
Ishai Dan-Cohen, Tomer Schlank
We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphism…
Rational motivic path spaces and Kim's relative unipotent section conjecture
Ishai Dan-Cohen, Tomer Schlank
We initiate a study of path spaces in the nascent context of "motivic dga's", under development in doctoral work by Gabriella Guzman. This enables us to reconstruct the unipotent f…
Mixed Tate motives and the unit equation II
Ishai Dan-Cohen
Over the past fifteen years or so, Minhyong Kim has developed a framework for making effective use of the fundamental group to bound (or even compute) integral points on hyperbolic…
The Heisenberg coboundary equation: appendix to Explicit Chabauty-Kim theory
Ishai Dan-Cohen, Stefan Wewers
Let p be a regular prime number, let Gp denote the Galois group of the maximal unramified away from p extension of Q, and let H_et denote the Heisenberg group over Qp with Gp-actio…
Mixed Tate motives and the unit equation
Ishai Dan-Cohen, Stefan Wewers
This is the second installment in a sequence of articles devoted to "explicit Chabauty-Kim theory" for the thrice punctured line. Its ultimate goal is to construct an algorithmic s…
A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves
Jennifer Balakrishnan, Ishai Dan-Cohen, Minhyong Kim +1
We state a conjectural criterion for identifying global integral points on a hyperbolic curve over in terms of Selmer schemes inside non-abelian cohomology functors wi…
Explicit Chabauty-Kim theory for the thrice punctured line in depth two
Ishai Dan-Cohen, Stefan Wewers
Let , and let denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for :…
Moduli of nondegenerate unipotent representations in characteristic zero
Ishai Dan-Cohen
With this work we initiate a study of the representations of a unipotent group over a field of characteristic zero from the modular point of view. Let be such a group. The stac…