Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky vs. Hanamura

We describe the Voevodsky's category $DM^{eff}_{gm}$ of motives in terms of Suslin complexes of smooth projective varieties. This shows that Voeovodsky's $DM_{gm}$ is anti-equivalent to Hanamura's one. We give a description of any triangulated subcategory of $DM^{eff}_{gm}$ (including the category of effective mixed Tate motives). We descibe 'truncation' functors $t_N$ for $N>0$. $t=t_0$ generalizes the weight complex of Soule and Gillet; its target is $K^b(Chow_{eff})$; it calculates $K_0(DM^{eff}_{gm})$, and checks whether a motive is a mixed Tate one. $t_N$ give a weight filtration and a 'motivic descent spectral sequence' for a large class of realizations, including the 'standard' ones and motivic cohomology. This gives a new filtration for the motivic cohomology of a motif. For 'standard realizations' for $l,s\ge 0$ we have a nice description of $W_{l+s}H^i/W_{l-1}H^i(X)$ in terms of $t_s(X)$. We define the 'length of a motif' that (modulo standard conjectures) coincides with the 'total' length of the weight filtration of singular cohomology. Over a finite field $t_0Q$ is (modulo Beilinson-Parshin conjecture) an equivalence.Comment: Several linguistic corrections made; section 2.3 was corrected als

Algebraic K-theory of endomorphism rings

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let Y\ra X be a covariant morphism of objects in ${\mathcal C}$. Then $K_n\big(_{\mathcal C}(X\oplus Y)\big)\simeq K_n\big(_{{\mathcal C},Y}(X)\big)\oplus K_n\big(_{\mathcal C}(Y)\big)$ for all $1\le n\in \mathbb{N}$, where $_{{\mathcal C},Y}(X)$ is the quotient ring of the endomorphism ring $_{\mathcal C}(X)$ of $X$ modulo the ideal generated by all those endomorphisms of $X$ which factorize through $Y$. Moreover, let $R$ be a ring with identity, and let $e$ be an idempotent element in $R$. If $J:=ReR$ is homological and $_RJ$ has a finite projective resolution by finitely generated projective $R$-modules, then $K_n(R)\simeq K_n(R/J)\oplus K_n(eRe)$ for all $n\in \mathbb{N}$. This reduces calculations of the higher algebraic $K$-groups of $R$ to those of the quotient ring $R/J$ and the corner ring $eRe$, and can be applied to a large variety of rings: Standardly stratified rings, hereditary orders, affine cellular algebras and extended affine Hecke algebras of type $\tilde{A}$.Comment: 21 pages. Representation-theoretic methods are used to study the algebraic K-theory of ring

Framed transfers and motivic fundamental classes

We relate the recognition principle for infinite P1-loop spaces to the theory of motivic fundamental classes of Deglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with An/(An-0), and the Gysin transfers defined via Verdier's deformation to the normal cone. We then introduce the category of finite R-correspondences for R a motivic ring spectrum, generalizing Voevodsky's category of finite correspondences and Calmes and Fasel's category of finite Milnor-Witt correspondences. Using the formalism of fundamental classes, we show that the natural functor from the category of framed correspondences to the category of R-module spectra factors through the category of finite R-correspondences

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

Вплив легувальної добавки на теплофізичні та реологічні властивості полімерної композиції, що не містить галогенів, для ізоляції та оболонок кабелів

Introduction. The demand for halogen-free fire-resistant compositions for the manufacture of fire-retardant wires and cables is constantly growing. Problem. Therefore, the creation and further processing of these materials is an urgent problem. Goal. The aim of the article is to study the effect of the doping additive on the thermophysical and rheological properties of halogen-free compositions for power cables with voltage 1 kV with the determination of both the temperatures of phase and structural transformations of polymer compositions. Methodology. Experiments investigating the phase transformations were carried out with the help device of thermogravimetric analysis and differential scanning calorimetry TGA/DSC 1/1100 SF of METTLER TOLEDO company. Rheological studies of polymeric materials were conducted by using the method of capillary viscosimetry in the device IIRT–AM. Results. The influence of the doping additive on the formation of the supramolecular structure of the filled polymer compositions for cable products was determined, that resulted in the temperature increase of the decomposition beginning by 11 °С and the end of decomposition by 7 °С. Originality. The effect of a doping additive on reducing the effective melt viscosity of a polymer composition from 6·104 to 1·104 Pa·s with increasing shear rate has been shown for the first time. The shear rate of the polymer composition containing the doping additive increases from 0.5 to 20 s–1 with increasing shear stress. Practical value. The research results provide an opportunity to reasonably approach the development of effective technological processes for the manufacture of the insulation and sheaths of power cables from halogen-free polymer compositions.Попит на вогнестійкі композиції, що не містять галогенів, для виготовлення пожежобезпечних проводів та кабелів безперервно зростає. Тому розробка цих матеріалів є актуальною проблемою. Метою статті є дослідження впливу легувальної добавки на теплофізичні та реологічні властивості композицій. Теплофізичні властивості визначено з використанням приладу TGA/DSC 1/1100 SF компанії METTLER TOLEDO. Реологічні дослідження полімерних матеріалів проведено методом капілярної віскозиметрії на приладі ИИРТ-АМ. Визначено вплив легувальної добавки на формування надмолекулярної структури наповнених полімерних композицій. Встановлено зниження ефективної в’язкості розплаву полімерної композиції в 6 разів зі зростанням швидкості зсуву в 40 разів при зміненні температури від 150 до 190 °С. Швидкість зсуву полімерної композиції з легувальною добавкою зростає в 40 разів з підвищенням напруження зсуву в 9 разів. Результати досліджень дають можливість обґрунтовано підходити до розроблення ефективних технологічних процесів виготовлення ізоляції та оболонок силових кабелів

Motivic Eilenberg-Maclane spaces

This paper is the second one in a series of papers about operations in motivic cohomology. Here we show that in the context of smooth schemes over a field of characteristic zero all the bi-stable operations can be obtained in the usual way from the motivic reduced powers and the Bockstein homomorphism.Comment: This version is very close to the final version accepted to the publication in Publ. IHE

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

Twenty Years of Galactic Observations in Searching for Bursts of Collapse Neutrinos with the Baksan Underground Scintillation Telescope

The results of twenty-year-long Galactic observations in neutrino radiation are summarized. Except for the recording of a neutrino signal from the supernova SN 1987A, no Galactic bursts of collapse neutrinos have been detected. An upper bound on the mean frequency of gravitational collapses in our Galaxy was obtained, $f_{collapse} (90$.Comment: latex, 7 pages, 2 eps figure

Hermitian K-theory and 2-regularity for totally real number fields

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8. In both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.Comment: To appear in Mathematische Annale