Geometric Characterization of Rings with Krull Dimension $\leq 1$
In this paper, we provide a new characterization of noetherian rings with Krull dimension $\leq 1$ in terms of its spectrum.
math.AC↗
arXiv subjects
Jesús Martín Ovejero
Publications and source records attributed to Jesús Martín Ovejero.
On the subalgebra of invariant elements: finiteness and immersions
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation $ρ:\underline{G}_{R}\rightarrow \underline{\textrm{Aut}}_{\textrm{Mod}(R)}(M)$. For the graded $T$-algebra $A$, defined as $ A := \left( S_{T}^{\bullet} (M^{\vee} \otimes_{R}N )\right)^{G}, $ we determine the conditions under which the graded $T$-algebra $A$ is finitely generated, finitely presented, or flat. Furthermore, we establish the conditions under which a closed embedding of $\textrm{Proj} \ A$ into a projective space exists. Since we do not impose any Noetherian hypotheses, our results generalize those in the literature, providing new powerful tools regarding moduli problems.
math.AG↗
Coordinate rings of some $SL_2$-character varieties
We determine generators of the coordinate ring of $SL_2$-character varieties. In the case of the free group $F_3$ we obtain an explicit equation of the $SL_2$-character variety. For free groups $F_k$ we find transcendental generators. Finally, for the case of the 2-torus, we get an explicit equation of the $SL_2$-character variety and use the description to compute their E-polynomials.
math.AG↗