arXiv subjects

Umesh V Dubey

Publications and source records attributed to Umesh V Dubey.

4 recordsLinked to original sources

arXiv2025

The Balmer spectrum of integral permutation modules

We extend the analysis of Balmer and Gallauer on the tt-geometry of the small derived category of permutation modules for a finite group over a field to the setting of a commutative Noetherian base. In this general context, we provide a description of the tt-spectrum as a set and reduce the study of its topology to the elementary abelian case. Under certain mild additional assumptions on the ground ring, we further develop their theory of twisted cohomology, which enables us to realize the tt-spectrum as a Dirac scheme when restricted to elementary abelian $p$-groups.

math.RT↗

arXiv2023

Quot schemes and Fourier-Mukai transformation

We consider several related examples of Fourier-Mukai transformations involving the quot scheme. A method of showing conservativity of these Fourier-Mukai transformations is described.

math.AG↗

arXiv2022

On Perverse sheaves of a Coxeter hyperplane arrangement of type $\mathcal{A}_n$

Kapranov and schechtman gave quiver description of perverse sheaves on real hyperplane arrangements. We used this description to relate the perverse sheaves on Coxeter hyperplane arrangements of type $\mathcal A_n$ for different values of $n$. As a consequence we prove that the simple perverse sheaves whose stalk on open cells are zero are induced from the perverse sheaves on lower dimension arrangements.

math.AG↗

arXiv2022

Tensor weight structures and t-structures on derived categories of Noetherian schemes

We give a condition which characterises those weight structures on a derived category which come from a Thomason filtration on the underlying scheme. Weight structures satisfying our condition will be called $\otimes ^c$-weight structures. More precisely, for a Noetherian separated scheme $X$, we give a bijection between the set of compactly generated $\otimes ^c$-weight structures on $\mathbf{D} (\mathrm{Qcoh\hspace{1mm}}X)$ and the set of Thomason filtrations of $X$. We achieve this classification in two steps. First, we show that the bijection of Sťov\'ıček and Posp\'ıšil restricts to give a bijection between the set of compactly generated $\otimes ^c$-weight structures and the set of compactly generated tensor t-structures. We then use our earlier classification of compactly generated tensor t-structures to obtain the desired result. We also study some immediate consequences of these classifications in the particular case of the projective line. We show that in contrast to the case of tensor t-structures, there are no non-trivial tensor weight structures on $\mathbf{D}^b (\mathrm{Coh \hspace{1mm}} \mathbb{P}^1_k)$.

math.AG↗