Related papers: On periods: from global to local

For any scheme which is algebraic over a subfield of the complex numbers we here construct an homological regulator from Suslin homology to period homology and a higher cycle class map from Bloch's higher Chow group to the period…

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

This paper is the augmented notes of a course I gave jointly with Laurent Berger in Rennes in 2014. Its aim was to introduce the periods rings B crys and B dR and state several comparison theorems between{\'e}tale and crystalline or de Rham…

We show that coefficients in the Laurent series of Igusa Zeta functions are periods. This will be used in a subsequent paper (by P. Brosnan) to show that certain numbers occurring in study of Feynman amplitudes (upto gamma factors) are…

We introduce the concept of degree to classify the periods in the sense of Kontsevich. Using this notion we give some new understanding of some problems in transcendental number theory.

We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can…

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…

This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…

Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex…

We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman…

We describe complex conjugation on the primitive middle-dimensional algebraic de Rham cohomology of a smooth projective hypersurface defined over a number field that admits a real embedding. We use Griffiths' description of the cohomology…

For a linear algebraic group G over the field of rational numbers, we consider the period domains D classifying G-mixed Hodge structures, and construct the extended period domains as toroidal partial compactifications. We give an…

The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the quantum affine algebra associated with a complex simple Lie algebra. The unrestricted…

This report outlines a combinatorial recipe for computing the bases, whose elements are oriented polygons, of two cohomology spaces associated to multizeta values: the top dimensional de Rham cohomology of moduli spaces of genus 0 complex…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

We give an explicit construction of the p-adic de Rham comparison isomorphism for 1-motives. In particular, we prove that our construction recovers the classical de Rham comparison isomorphism and is functorial with respect to morphisms of…

We express a family of basic cellular integrals over moduli spaces of curves explicitly in terms of multiple zeta values, answering a question of Brown. Moreover, we study a priori the weights appearing in these integrals and find a…

We develop a $p$-adic theory of periods for 1-motives, extending the classical theory of complex periods into the non-archimedean setting. For 1-motives with good reduction over $p$-adic local fields, we construct a $p$-adic integration…

We give a characterization of groups with twisted p-periodic cohomology in terms of group actions on mod p homology spheres. An equivalent algebraic characterization of such groups is also presented.

We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories of finite-dimensional representations of quantum affine algebras of types $A_{2n-1}^{(1)}$ and $B_n^{(1)}$. Our proof relies in part…