arXiv subjects

Esha Gupta

Publications and source records attributed to Esha Gupta.

5 recordsLinked to original sources

arXiv2025

Semibricks and wide subcategories in extended module categories

For $d\geq 1$, we define semibricks and wide subcategories in the $d$-extended hearts of bounded $t$-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the $d$-extended heart is the $d$-extended module category $d\mbox{-}\mathrm{mod}\Lambda$ of a finite-dimensional algebra $\Lambda$ over a field, we define left/right-finite semibricks and left/right-finite wide subcategories in $d\mbox{-}\mathrm{mod}\Lambda$ and show bijections with $(d+1)$-term simple-minded collections, generalising the bijections between $2$-term simple-minded collections, left/right-finite wide subcategories and left/right-finite semibricks in $\mathrm{mod}\Lambda$. We use a relation between semibricks and silting complexes to characterise which mutations of $(d+1)$-term silting complexes are again $(d+1)$-term.

math.RT↗

arXiv2024

A restricted model for the bounded derived category of gentle algebras

We present a restricted model for the bounded derived category of gentle algebras that encodes the indecomposable objects and positive extensions between them. The model is then used to count the number of $d$-term silting objects for linearly oriented $A_n$, recovering the result that they are counted by the Pfaff-Fuss-Catalan numbers.

math.RT↗

arXiv2024

On $d$-term silting objects, torsion classes, and cotorsion classes

For a finite-dimensional algebra $\Lambda$ over an algebraically closed field $K$, it is known that the poset of $2$-term silting objects in $\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of functorially finite torsion classes in $\operatorname{mod}\Lambda$, and to that of complete cotorsion classes in $\mathrm{K}^{[-1,0]}(\operatorname{proj}\Lambda)$. In this work, we generalise this result to the case of $d$-term silting objects for arbitrary $d\geq 2$ by introducing the notion of torsion classes for extriangulated categories. In particular, we show that the poset of $d$-term silting objects in $\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of complete and hereditary cotorsion classes in $\mathrm{K}^{[-d+1,0]}(\operatorname{proj}\Lambda)$, and to that of positive and functorially finite torsion classes in $D^{[-d+2,0]}(\operatorname{mod}\Lambda)$, an extension-closed subcategory of $D^b(\operatorname{mod}\Lambda)$. We further show that the posets $\operatorname{cotors}\mathrm{K}^{[-d+1,0]}(\operatorname{proj}\Lambda)$ and $\operatorname{tors} D^{[-d+2,0]}(\operatorname{mod}\Lambda)$ are lattices, and that the truncation functor $\tau_{\geq -d+2}$ gives an isomorphism between the two.

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arXiv2022

Euclidean algorithm for a class of linear orders

Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an analogous correspondence with equimorphism classes of indecomposable finite rank discrete linear orders. We also introduce the class of \emph{finitely presented linear orders}-- the smallest subclass of finite rank linear orders containing $\mathbf 1$, $\omega$ and $\omega^*$ and closed under finite sums and lexicographic products. For this class we develop a generalization of the Euclidean algorithm where the \emph{width} of a linear order plays the role of the Euclidean norm. Using this as a tool we classify the isomorphism classes of finitely presented linear orders in terms of an equivalence relation on their presentations using \emph{3-signed trees}.

math.CO↗

arXiv2020

On the stable radical of some non-domestic string algebras

We introduce the concept of a prime band in a string algebra $Λ$ and use it to associate to $Λ$ its finite bridge quiver. Then we introduce a new technique of `recursive systems' for showing that a graph map between finite dimensional string modules lies in its stable radical. Further we study two classes of non-domestic string algebras in terms of some connectedness properties of its bridge quiver. `Meta-$\bigcup$-cyclic' string algebras constitute the first class that is essentially characterized by the statement that each finite string is a substring of a band. Extending this class we have `meta-torsion-free' string algebras that are characterized by a dichotomy statement for ranks of graph maps between string modules--such maps either have finite rank or are in the stable radical. Their stable ranks can only take values from $\{ω,ω+1,ω+2\}$.

math.RT↗