Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Jun, Jaiung"'
We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an idempotent semifield equivar
Externí odkaz:
http://arxiv.org/abs/2406.06933
Autor:
Borger, James, Jun, Jaiung
We set up some basic module theory over semirings, with particular attention to scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual definitions of line bundle do agree. W
Externí odkaz:
http://arxiv.org/abs/2405.18645
Autor:
Eyler, Mason, Jun, Jaiung
We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring several analogous notions, such as (unramified) Galois coverings and Frobenius elements. To a hypergraph $H$, one can naturally associate a bipartite graph $B_H$ encoding in
Externí odkaz:
http://arxiv.org/abs/2309.15873
Autor:
Hobby, David, Jun, Jaiung
We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T. Zhang: Does a system of homogeneous linear equations with more unknowns than
Externí odkaz:
http://arxiv.org/abs/2306.13232
The Picard group of an undirected graph is a finitely generated abelian group, and the Jacobian is the torsion subgroup of the Picard group. These groups can be computed by using the Smith normal form of the Laplacian matrix of the graph or by using
Externí odkaz:
http://arxiv.org/abs/2302.10327
We investigate quiver representations over $\mathbb{F}_1$. Coefficient quivers are combinatorial gadgets equivalent to $\mathbb{F}_1$-representations of quivers. We focus on the case when the quiver $Q$ is a pseudotree. For such quivers, we first use
Externí odkaz:
http://arxiv.org/abs/2301.07221
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including
Externí odkaz:
http://arxiv.org/abs/2203.01086
\emph{Proto-exact categories}, introduced by Dyckerhoff and Kapranov, are a generalization of Quillen exact categories which provide a framework for defining algebraic K-theory and Hall algebras in a \emph{non-additive} setting. This formalism is wel
Externí odkaz:
http://arxiv.org/abs/2202.01573
Autor:
Jun, Jaiung, Sistko, Alex
A quiver representation assigns a vector space to each vertex, and a linear map to each arrow. When one considers the category $\textrm{Vect}(\mathbb{F}_1)$ of vector spaces ``over $\mathbb{F}_1$'' (the field with one element), one obtains $\mathbb{F
Externí odkaz:
http://arxiv.org/abs/2112.06291
