Related papers: Adjoint rings are finitely generated
We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as…
We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.
We show that every finitely generated cohomologically trivial module over $RG$, where $G$ is a finite $p$-group and $R$ is a $p$-adic ring, splits as the direct sum of a finite cohomologically trivial $RG$-module and a free $RG$-module.…
We prove Koll\'ar-type effective basepoint-free theorems for quasi-log canonical pairs.
We discuss the problem on the connectedness of various webs of lattice polytopes by introducing a geometric point of view from the toric Mori theory. To this end, we provide a combinatorial description of toric Sarkisov links in terms of…
Here we analyze a proper 2-generated core in a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank. We ultimately show that such a group is strongly embedded and the ambiant group is…
We give a twisted version of the Kawamata semi-positivity theorem by the $\mathbb{Q}$-line bundle with a vanishing Lelong number at every point. Moreover, we apply the result to the finite generation problem for canonical rings of Birkar's…
This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely…
We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.
By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic…
Let f be a generically finite morphism from X to Y. The purpose of this paper is to show how the O_Y algebra structure on the push forward of O_X controls algebro-geometric aspects of X like the ring generation of graded rings associated to…
We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which…
The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative…
We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear…
Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety $\mathbb E^1$ whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely…
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of the plane at distinct points lying on a (possibly reducible) cubic.
In 1968, Milnor conjectured that a complete noncompact manifold with nonnegative Ricci curvature has a finitely generated fundamental group. The author applies the Excess Theorem of Abresch and Gromoll (1990), to prove two theorems. The…
Let $<X>$ be the free monoid on a generating set $X$, and suppose one adjoins to $<X>$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorithm which yields a normal form for elements of the resulting…
The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the…
For all infinite rings $R$ that are finitely generated over $\mathbb{Z}$, we show that Hilbert's tenth problem has a negative answer. This is accomplished by constructing elliptic curves $E$ without rank growth in certain quadratic…