Related papers: The telescope conjecture for semihereditary commut…

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

We give a series of successively weaker conjectures on the cohomology ring of the Grassmannian, starting with the Hilbert series of a certain natural filtration.

This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

The class of semi-hereditary rings is an important class of rings in theories that do not assume the Noetherian condition, such as perfectoid ring theory. We prove several results concerning the structure theory of this class, focusing on…

This paper has been withdrawn by the authors due to an error in Section 7.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived…

This paper is wrong and is therefore withdrawn.

We show that the Gromov-Lawson-Rosenberg conjecture for the Semi-Dihedral group of order 16 is true.

This paper has been withdrawn by the author due to a mistake in the section 4.

Perverse-Hodge complexes are objects in the derived category of coherent sheaves obtained from Hodge modules associated with Saito's decomposition theorem. We study perverse-Hodge complexes for Lagrangian fibrations and propose a symmetry…

This paper has been withdrawn due to a error in Theorem 3.1.

Title: An unlikely result Authors: T.M. Other Comments: This paper has been withdrawn Abstract: This paper has been withdrawn by the author due to the fact that some of the results turned out to be known.

For every imprimitive complex reflection group of rank 2, we construct a semi-orthogonal decomposition of the derived category of the associated global quotient stack which categorifies the usual decomposition of the orbifold cohomology…

We consider T(x), a tensor of arbitrary rank that is symmetric in all of its indices and conserved in the sense that the divergence on any one index vanishes. Our conjecture is that all integral moments of this tensor will vanish if the…

We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…

This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.

Hou and Liu developed a telescoping method to prove the congruence of partial sums of P-recursive sequences. We release the requirement on the telescoper and utilize the congruence of the sequence. With this approach, we are able to confirm…

We call a triangulated category \emph{hereditary} provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the…

In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a commutative noetherian ring $R$ and complexes of $R$-modules…