Endomorphism ≈ Endomorphism
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Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties Open
Given a quasiprojective variety $X$ with only Kawamata log terminal singularities, we study the obstructions to extending finite étale covers from the smooth locus $X_{\\mathrm{reg}}$ of $X$ to $X$ itself. A simplified version of our main …
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Dimer models and cluster categories of Grassmannians Open
We associate a dimer algebra $A$ to a Postnikov diagram $D$ (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian ${\\rm Gr}(k,n)$. We show that $A$ is isomorphic to the endomorphism algebra of a cor…
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Self-dual Leonard pairs Open
Let F denote a field and let V denote a vector space over F with finite positive dimension. Consider a pair A, A* of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an irreducible tridiagonal fas…
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Higher Frobenius-Schur indicators for pivotal categories Open
We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the …
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Asymptotic solutions in asymptotic safety Open
We explain how to find the asymptotic form of fixed point solutions in\nfunctional truncations, in particular $f(R)$ approximations. We find that\nquantum fluctuations do not decouple at large $R$, typically leading to\nelaborate asymptoti…
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Rigorous computation of the endomorphism ring of a Jacobian Open
We describe several improvements to algorithms for the rigorous computation\nof the endomorphism ring of the Jacobian of a curve defined over a number\nfield.\n
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On the Breuil–Mézard conjecture Open
We give a new local proof of the Breuil–Mézard conjecture for $2$ -dimensional representations of the absolute Galois group of $\\mathbb{Q}_{p}$ , when $p\\ge5$ and the representation has scalar endomorphisms.
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GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS Open
Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_{p}}$ of the finite field of prime order $p$ and let $F:\mathbf{G}\rightarrow \mathbf{G}$ be a Frobenius endomorphism with $G=\mathbf…
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Commensurating endomorphisms of acylindrically hyperbolic groups and applications Open
We prove that the outer automorphism group Out (G) is residually finite when the group G is virtually compact special (in the sense of Haglund and Wise) or when G is isomorphic to the fundamental group of some compact 3-manifold. To prove …
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On the Mackey formula for connected centre groups Open
Let 𝐆 {\mathbf{G}} be a connected reductive algebraic group over 𝔽 ¯ p {\overline{\mathbb{F}}_{p}} and let F : 𝐆 → 𝐆 {F:\mathbf{G}\to\mathbf{G}} be a Frobenius endomorphism endowing 𝐆 {\mathbf{G}} with an 𝔽 q {\mathbb{F…
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Grassmann extensions of Yang–Baxter maps Open
In this paper we show that there are explicit Yang-Baxter maps with\nDarboux-Lax representation between Grassmann extensions of algebraic varieties.\nMotivated by some recent results on noncommutative extensions of Darboux\ntransformations…
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On the lambda algebra and Singer's cohomological transfer Open
Write $\mathbb A$ for the 2-primary Steenrod algebra, which is the algebra of stable natural endomorphisms of the mod 2 cohomology functor on topological spaces. Working at the prime 2, computing the cohomology of $\mathbb A$ is an importa…
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Arithmetic degrees and dynamical degrees of endomorphisms on surfaces Open
For a dominant rational self-map on a smooth projective variety defined over\na number field, Shu Kawaguchi and Joseph H. Silverman conjectured that the\ndynamical degree is equal to the arithmetic degree at a rational point whose\nforward…
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Computing endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs Open
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems.We give a n…
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Geometric realizations of quiver algebras Open
In this paper we construct strong exceptional collections of vector bundles\non smooth projective varieties that have a prescribed endomorphism algebra. We\nprove the construction problem always have a solution. We consider some\napplicati…
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Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields Open
We study the birational properties of geometrically rational surfaces from a\nderived categorical point of view. In particular, we give a criterion for the\nrationality of a del Pezzo surface over an arbitrary field, namely, that its\nderi…
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Silting modules and ring epimorphisms Open
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism whi…
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Supersingular curves with small noninteger endomorphisms Open
We introduce a special class of supersingular curves over ކ p 2 , characterized by the existence of noninteger endomorphisms of small degree.We prove a number of properties about this set.Most notably, we can partition this set into subs…
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C^*-Algebras of algebraic dynamical systems and right LCM semigroups Open
We introduce algebraic dynamical systems, which consist of an action of a\nright LCM semigroup by injective endomorphisms of a group. To each algebraic\ndynamical system we associate a C*-algebra and describe it as a semigroup\nC*-algebra.…
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A class of Drazin inverses in rings Open
A strongly direct sum decomposition given by a strongly nil-clean endomorphism motivates us to introduce a class of new Drazin inverses, which is called strong Drazin inverse. In this paper, some basic properties of the strong Drazin inver…
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On the Categorical Entropy and the Topological Entropy Open
To an exact endofunctor of a triangulated category with a split-generator,\nthe notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which\nis a (possibly negative infinite) real-valued function of a real variable. In\nthis …
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On the geometry of the automorphism groups of affine varieties Open
This article is a survey on ind-varieties and ind-groups introduced by Shafarevich in 1965, with a special emphasis on automorphism groups of affine varieties and actions of ind-groups on ind-varieties. We give precise definitions and comp…
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Theory of interleavings on categories with a flow Open
The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal et al. as a metric on the class of persistence modules parametrized over the real line. Bubenik et al. subsequently extended the def…
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On the structure tensors of almost contact B-metric manifolds Open
The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspace…
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ALGEBRAIC YUZVINSKI FORMULA Open
Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is the so-called Yuzvinski Formula, which is the key step in finding the topological entropy of any compact group…
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Categorified Young symmetrizers and stable homology of torus links Open
We show that the triply graded Khovanov-Rozansky homology of the torus link\n$T_{n,k}$ stablizes as $k\\to \\infty$. We explicitly compute the stable homology\n(as a ring), which proves a conjecture of Gorsky-Oblomkov-Rasmussen-Shende. To\…
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The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane Open
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.
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A (dummy’s) guide to working with gapped boundaries via (fermion) condensation Open
A bstract We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the spe…
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Full-rank affine invariant submanifolds Open
We show that every $\\operatorname{GL}(2,R)$ orbit closure of translation surfaces is a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jacobians have extra endomorphisms. We use this resul…
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Noncommutative Auslander theorem Open
In the 1960s Maurice Auslander proved the following important result. Let $R$ be the commutative polynomial ring $\mathbb {C}[x_1,\dots ,x_n]$, and let $G$ be a finite small subgroup of $\textrm {GL}_n(\mathbb {C})$ acting on $R$ naturally…