Related papers: Motivic Toda brackets
The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these…
High rank solutions to the 2D Toda Lattice System are constructed simultaneously with the effective calculation of coefficients of the high rank commuting ordinary difference operators. Our technic is based on the study of discrete dynamics…
In this note, we describe motivic cell structures arising from the Bialynicki-Birula decomposition. This provides a description of the stable A^1-homotopy types of smooth projective G_m-varieties where the G_m-action has isolated fixed…
A detailed consideration of the maximally nonabelian Toda systems based on the classical semisimple Lie groups is given. The explicit expressions for the general solution of the corresponding equations are obtained.
There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras…
We discuss the structure of integral etale motivic cohomology groups of smooth and projective schemes over algebraically closed fields, finite fields, local fields, and arithmetic schemes.
A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…
We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the…
A connection between the finite ultradiscrete Toda lattice and the box-ball system is extended to the case where each box has own capacity and a carrier has a capacity parameter depending on time. In order to consider this connection, new…
For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admits an intrinsic interpretation in terms of contact loci of…
We develop a theory of modulus triples, for future motivic applications.
A box-ball system with more than one kind of balls is obtained by the generalized periodic discrete Toda equation (pd Toda eq.). We study the pd Toda equation in view of algebraic geometry. The time evolution of pd Toda eq. is linearized on…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is…
We propose an extension of pure type systems with an algebraic presentation of inductive and co-inductive type families with proper indices. This type theory supports coercions toward from smaller sorts to bigger sorts via explicit type…
We construct two different incompatible Poisson pencils for the Toda lattice by using known variables of separation proposed by Moser and by Sklyanin.
In a non-compact setting, the notion of hyperbolicity, and the associated structure of stable and unstable manifolds (for unbounded orbits), is highly dependent on the choice of metric used to define it. We consider the simplest version of…
The Hamiltonian structure of the two-dimensional dispersionless Toda hierarchy is studied, this being a particular example of a system of hydrodynamic type. The polynomial conservation laws for the system turn out, after a change of…