326 citations
- Max Planck SocietyDE74 papers
- Max Planck Institute for Mathematics in the SciencesDE13 papers
- Collège de FranceFR3 papers
- Centre National de la Recherche ScientifiqueFR2 papers
- Northwestern UniversityUS2 papers
- Princeton UniversityUS2 papers
- The University of AdelaideAU2 papers
- University of OregonUS2 papers
- Algebra Bernays UniversityHR1 paper
- Baylor UniversityUS1 paper
- Brown UniversityUS1 paper
- Central China Normal UniversityCN1 paper
7 papers · 2 filters
Renormalization and motivic Galois theory
Alain Connes, Matilde Marcolli
We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain `` motivic Galois group'', which is uniquely determi…
On the image of l-adic Galois representations for abelian varieties of type I and II
Grzegorz Banaszak, Wojciech Gajda, Piotr Krason
In this paper we investigate the image of the -adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or I…
Around Pelikan's conjecture on very odd sequences
Pieter Moree, Patrick Sole
Very odd sequences were introduced in 1973 by J. Pelikan who conjectured that there were none of length >=5. This conjecture was disproved by MacWilliams and Odlyzko in 1977 who pr…
On the distribution of the order and index of g(mod p) over residue classes III
Pieter Moree
For a fixed rational number g and integers a and d the sets N_g(a,d), respectively R_g(a,d), of primes p for which the order, respectively the index of g(mod p) is congruent to a(m…
From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
Alain Connes, Matilde Marcolli
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arit…
Galois modules arising from Faltings's strict modules
Victor Abrashkin
Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was introduced recently by Falting…