Related papers: On surjectivity in tensor triangular geometry

Suppose $X$ is a smooth, proper, geometrically connected curve over $\mathbb F_q$ with an $\mathbb F_q$-rational point $x_0$. For any $\mathbb F_q^{\times}$-character $\sigma$ of $\pi_1(X)$ trivial on $x_0$, we construct a functor $\mathbb…

We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map sending (x,y) to the product of the Nth powers of x and y is…

A theorem of Jannsen asserts that if a smooth projective variety has injective cycle class maps, it has surjective cycle class maps. The object of this note is to present a version of Jannsen's theorem for singular quasi--projective…

We discuss gluing of objects and gluing of morphisms in tensor triangulated categories. We illustrate the results by producing, among other things, a Mayer-Vietoris exact sequence involving Picard groups.

We give a definition of a coherent adjunction in a $4$-category consisting of a finite list of $k$-morphisms for $k\leq 4$, plus equations beetween $4$-morphisms. We prove that the restriction map from the space of coherent adjunctions in a…

We define the spectrum of a tensor triangulated category $K$ as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects…

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…

Given a rigidly-compactly generated tensor-triangulated category whose Balmer spectrum is finite dimensional and Noetherian, we construct a torsion model for it, which is equivalent to the original tensor-triangulated category. The torsion…

In recent work, for a triangulated category $\cT$, the author introduced a topological space $\tSpec(\cT)$ which we call the triangular spectrum of $\cT$ as a tensor-free analog of the Balmer spectrum for a tensor triangulated category. In…

We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the…

We present an elementary proof of the fact that every torsor for an affine group scheme over an algebraically closed field is trivial. This is related to the uniqueness of fibre functors on neutral tannakian categories.

We prove the global triangulation conjecture for families of refined p-adic representations under a mild condition. That is, for a refined family, the associated family of (phi, Gamma)-modules admits a global triangulation on a Zariski open…

We prove surjectivity of the comparison map from continuous bounded cohomology to continuous cohomology for Hermitian Lie groups with finite center. For general semisimple Lie groups with finite center, the same argument shows that the…

Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…

We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].

We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…

We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the homological spectrum is homeomorphic to a quotient of the…

The current work is motivated by the papers $[B_3]$, $[B_6]$, $[Be]$, $[Be-Tu]$. In particular, using Theorem 3.7 of $[B_3]$ and methods developed in this paper, the spectral and strong homology groups of continuous maps were defined and…

Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In…

A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore--Seiberg relations. A functor to N is constructed…