Coleman integration using the Tannakian formalism

By A. Besser. 2000

94 citations recorded by the source corpus.

Abstract. We use a new idea to construct a theory of iterated Coleman functions on overconvergent spaces with good reduction in any dimension. A Coleman function in this theory consists of a unipotent differential equation, a functional on the underlying bundle and a solution to the equation on a residue class. The new idea is to use the theory of Tannakian categories and the action of Frobenius to analytically continue solutions of the differential equation to all residue classes.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6880dd8d3906712cb70d61432ec293532765589f

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In Geometry and Topology

1. Jennifer S. Balakrishnan
2. Netan Dogra
3. Ishai Dan-Cohen
4. Stefan Wewers
5. H. Furusho
6. Minhyong Kim
7. F. Pop

In Statistical and Nonlinear Physics

1. H. Furusho
2. Ishai Dan-Cohen
3. Jennifer S. Balakrishnan
4. Minhyong Kim
5. Stefan Wewers
6. Netan Dogra

Citations in the corpus

• A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves (2012, methodology): “ ∈F0PdR n (x)(Qp), we define α(x) to be the class of the unique Qp-point uof UndR satisfying pcru= pH. A NON-ABELIAN CONJECTURE 13 3.4.4. It follows from Besser’s interpretation of Coleman integration [Bes] that αpulls back algebraic functions on UdR n /F 0 to Coleman functions on X(Zp). These tend t”
• p -adic multiple zeta values II. Tannakian interpretations (2005, methodology): “have an action of the geometric Frobenius F robp of p. Since the eigenvalues of the F robp-action on H 1 ´et (X K ,Ql) are positive weight Weil numbers, we obtain a unique Frobenius invariant path e p,∗′ by an inductive construction same to [Bes]§3”
• p-adic multiple zeta values I. (2004, background): “2.3. For other nice expositions of his theory, see [ Bes2 ] Sect.”
• The motivic fundamental group of P1∖{0,1,∞} and the theorem of Siegel (2005, background): “For any points y, y′ ∈ P1(k), we have the group of isomorphisms from sy to sy′ giving rise to the crystalline fundamental groups π1,cr(Y, y), which are pro-unipotent algebraic groups over F, and the torsors of paths π1,cr(Y, y, y′) ([2], Sect.”
• Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties (2017, methodology): “By Besser’s Tannakian interpretation of iterated Coleman integration [8], the relation between trivialising the Frobenius structure and p-adic integration is well understood.”