Related papers: On Beilinson's Hodge and Tate conjectures for open…

We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.

We survey recent developments on the Restriction conjecture.

Minor technical changes. Section 4 improved.

Along the lines of Hodge and Tate conjectures, Beilinson conjectured that in the qth cohomology all the weight 2q Hodge cycles of a smooth complex variety and all the weight 2q Tate cycles of a smooth variety over a finitely generated field…

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.

This paper has been withdrawn by the author; its content is properly cantained in the paper arXiv:0706.4447, entitled "Pure motives, mixed motives and extensions of motives associated to singular surfaces", and submitted on June 29, 2007.

The paper was withdrawn because of its significant overlap with a paper appeared recently.

A technical flaw was found in this paper, and it has been withdrawn. It is intended that a modified version will be submitted soon.

In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such…

Revision contains rewording of selected text

In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper intersection over a regular ring based on the intersection…

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.

We prove that the d\'evissage property holds for periodic cyclic homology for a local complete intersection embedding into a smooth scheme. As a consequence, we show that the complexified topological Chern character maps for the bounded…

We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.

We consider the overlap of Bethe vectors of the XXX spin chain with a diagonal twist and the modified Bethe vectors with a general twist. We find a determinant representation for this overlap under one additional condition on the twist…

We propose a theory of contact invariants and open string invariants, assuming that the almost complex $J$ is either non-degenerate or of Bott-type. We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$ on periodic…

Recently Engel et al. (2025) have shown that the integral Hodge conjecture fails for very general abelian varieties. Using Deligne's theory of absolute Hodge cycles, we deduce a similar statement for the integral Tate conjecture.