Related papers: On rank $2$ hypergeometric motives

We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif $M$ implies…

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…

We study the middle convolution of local systems and realize special linear groups as Galois groups over the rationals. In the Appendix to this paper, written jointly with Stefan Reiter, we prove the existence of a new motivic local system…

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…

We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main…

In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a…

These memos include the research on $\mathcal{G}_{\mathbb{S}}^{alg}$-scheme theory, the definition of symplectic motives over $\mathcal{G}_{\mathbb{S}}^{alg}$-schemes and symplectic motivic cohomology. This presents a new research…

We recognize certain special hypergeometric motives, related to and inspired by the discoveries of Ramanujan more than a century ago, as arising from Asai $L$-functions of Hilbert modular forms.

In this article we study motives corresponding to the moduli stacks of G-shtukas and their local models. In particular we deal with the question of describing their motivic fundamental invariants. As an application, we provide a criterion…

We study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes $\A$. The cohomology plays an important role for the theory of generalized hypergeometric functions. We combine several…

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from…

We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and…

We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair…

In this paper, first we obtain some new and interesting results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally of finite type projective module is continuous with…

We consider Fano sevenfolds $Y$ obtained by intersecting the Grassmannian $\hbox{Gr}(3,6)$ with a codimension 2 linear subspace (with respect to the Pl\"ucker embedding). We prove that the motive of $Y$ is Kimura finite-dimensional. We also…

Let $X$ be a smooth projective curve over a field of characteristic zero and let $\mathcal D$ be an effective divisor on $X$. We calculate motivic classes of various moduli stacks of parabolic vector bundles with irregular connections on…

The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic…

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…