Related papers: A family of infinite degree tt-rings

An infinite family of nonschurian separable association schemes is constructed.

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

We construct new families of groups with property (T) and infinitely many alternating group quotients. One of those consists of subgroups of $\mathrm{Aut}(\mathbf F_{p}[x_1, \dots, x_n])$ generated by a suitable set of tame automorphisms.…

It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.

In this note, we prove that there exist infinite dimensional excellent rings.

We develop the theory of group graded division ring parallel to the one by P. Cohn for (ungraded) division rings.

We construct infinite families of abstract regular polytopes of type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain…

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an…

After constructing a splitting tower for separable commutative ring objects in tensor-triangulated categories, we define and study their degree.

We construct $(P_2)$-closed groups acting on $T_3$ in which all edge inversions have infinite order. This provides a negative answer to a question posed by Tornier. We also construct a family of $(P_2)$-closed groups for which the smallest…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

We present a method to construct infinite families of entangling $2$-qudit gates, and amongst them entangling $2$-qudit gates which satisfy the Yang-Baxter equation. We show that, given $2$-qudit gates $c$ and $d$, if $c$ or $d$ is…

Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $M_g$ (and in fact that of $M_{g,2}$). One immediate consequence of these relations is that the classes…

We address the problem of constructing a simple holomor- phic eta quotient of a given level N . Such constructions are known for all cubefree N . Here, we provide such constructions for arbitrarily large prime power levels. As a…

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

We introduce a class of polytopes that we call chainlink polytopes and which allow us to construct infinite families of pairs of non isomorphic rational polytopes with the same Ehrhart quasi-polynomial. Our construction is based on circular…

By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category $\T$ is equivalent to the topological structure of its Balmer spectrum $\spc \T$. Motivated by this theorem, we discuss…

We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel's circle problem (1959). The proof relies on a…

We construct a faithfully flat algebra over the infinite polynomial ring on an algebraically closed field that is not descendable.