Zobrazeno 1 - 10
of 186
pro vyhledávání: '"13D15"'
Classically, the splitting principle says how to pull back a vector bundle in such a way that it splits into line bundles and the pullback map induces an injection on $K$-theory. Here we categorify the splitting principle and generalize it to the con
Externí odkaz:
http://arxiv.org/abs/2410.05598
Linear hypersurfaces over a field $k$ have been playing a central role in the study of some of the challenging problems on affine spaces. Breakthroughs on such problems have occurred by examining two difficult questions on linear polynomials of the f
Externí odkaz:
http://arxiv.org/abs/2405.07205
Autor:
Puthenpurakal, Tony J.
In this paper we give bountiful examples of Gorenstein local rings $A$ and $B$ such that there is a triangle equivalence between the stable categories \underline{CM}($A$), \underline{CM}($B$).
Externí odkaz:
http://arxiv.org/abs/2403.05097
Autor:
Mattoo, Amal
If an element of the Grothendieck group of the derived category of a scheme is locally represented by perfect complexes, then can the original element be represented by a perfect complex? We provide a counterexample on a projective variety of dimensi
Externí odkaz:
http://arxiv.org/abs/2311.12254
Autor:
Tarizadeh, Abolfazl
Let $G$ be the Grothendieck group of a commutative monoid $M$. We prove that for any multiplicative set $S$ of homogeneous elements of an $M$-graded ring $R=\bigoplus\limits_{m\in M}R_{m}$, then the localization ring ...
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2309.15620
Autor:
Puthenpurakal, Tony J.
Let $(A,\mathfrak{m})$ be a short Artin local ring (i.e., $\mathfrak{m}^3 = 0$ and $\mathfrak{m}^2 \neq 0$). Assume $A$ is not a hypersurface ring. We show there exists $c_A \geq 2$ such that if $M$ is any finitely generated module with bounded betti
Externí odkaz:
http://arxiv.org/abs/2307.16132
A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich modules split. In this paper we initiate the study of Ulrich split rings. We prove several necessary or sufficient criteria for this property, linking it to syz
Externí odkaz:
http://arxiv.org/abs/2210.03872
Autor:
Tarizadeh, Abolfazl
The main goal of this article is to investigate the Grothendieck groups, especially the Grothendieck ring $K_{0}(R)$, the Picard group $\Pic(R)$ and the ideal class group $\Cl(R)$ of a given commutative ring $R$. Among the main results, we obtain a g
Externí odkaz:
http://arxiv.org/abs/2210.02951
Autor:
Puthenpurakal, Tony J.
Let $(A,\mathfrak{m})$ be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of $A$ is known then by a result of Auslander and Reiten one can explicity compute $G(A)$ the Grothendieck group of finitely ge
Externí odkaz:
http://arxiv.org/abs/2209.11566
Autor:
Zakharevich, Inna
We construct a monoidal structure on the category of assemblers. As an application of this, we construct a derived local zeta-function which takes a variety over a finite field to the set of points over the separable closure, and use the structure of
Externí odkaz:
http://arxiv.org/abs/2209.08640