Related papers: Heights of mixed motives

We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.

In this paper,we count the rational points on the weighted projective spaces defined over number fields w.r.t. ``size''. An asymptotic formula which generalizes the result of Schanuel's ``Heights in number fields'' is obtained. Furthermore,…

We define a notion of coordinatization for $\aleph_0$-categorical structures which is, like Lie coordinatized structures in [2], a certain kind of expansion of a tree. We show that a structure which is coordinatized, in a certain strong…

We give a simple naming argument for establishing lower bounds on the combinatorial distance between (positive) braid words.

We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we express their motivic nearby fibers in terms of the geometric data…

For noetherian schemes of finite dimension over a field of characteristic exponent $p$, we study the triangulated categories of $\mathbf{Z}[1/p]$-linear mixed motives obtained from cdh-sheaves with transfers. We prove that these have many…

We compute the Ext group of the (filtered) Ogus category over a number field $K$. In particular we prove that the filtered Ogus realisation of mixed motives is not fully faithful.

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

Building on earlier work concerning the motives of $G$-bundles, we study the structure of motives associated with certain classes of $G$-varieties. In particular, we show that the corresponding motives lie within the category of mixed-Tate…

We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."

We compute numerically the homology of several graph complexes in low loop orders, extending previous results.

In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.

We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.

For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed.

We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units.

We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.

Let $\F_p = \Z/p\Z$. The \emph{height} of a point $\mathbf{a}=(a_1,..., a_d) \in \F_p^d$ is $h_p(\mathbf{a}) = \min \left\{\sum_{i=1}^d (ka_i \mod p) : k=1,...,p-1\right\}.$ Explicit formulas and estimates are obtained for the values of the…

In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…

We explain the role of the boundary motive in the construction of certain Chow motives, and of extensions of Chow motives. Our two main examples concern proper, singular surfaces and fibre products of a universal elliptic curve.