Related papers: Notes on Frobenius stable direct images

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…

Positive modalities in systems in the vicinity of S4 and S5 are investigated in terms of categorial proof theory. Coherence and maximality results are demonstrated, and connections with mixed distributive laws and Frobenius algebras are…

In this article we develop the cotangent complex and (co)homology theories for spectral categories. Along the way, we reproduce standard model structures on spectral categories. As applications, we show that the invariants to descend to…

In this paper, we prove the weak positivity theorem in positive characteristic when the canonical ring of the geometric generic fiber $F$ is finitely generated and the Frobenius stable canonical ring of $F$ is large enough. As its…

We study representation stability in the sense of Church, Ellenberg, and Farb \cite{FI-module} through the lens of symmetric function theory and the different symmetric function bases. We show that a sequence, $(F_n)_n$, where $F_n$ is a…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…

This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric data and, building on this geometric viewpoint, we prove…

Syntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue…

We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves.

In this article we define stable supercurves and super stable maps of genus zero via labeled trees. We prove that the moduli space of stable supercurves and super stable maps of fixed tree type are quotient superorbifolds. To this end, we…

We generate synthetic images with the "Stable Diffusion" image generation model using the Wordnet taxonomy and the definitions of concepts it contains. This synthetic image database can be used as training data for data augmentation in…

Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated application of the character theory of finite groups. In this…

A countable discrete group is said to be Frobenius stable if every function from the group to unitary matrices that is "almost multiplicative" in the Frobenius norm is "close" to a unitary representation in the Frobenius norm. The purpose…

The paper deals with a class of periods, Frobenius constants, which describe monodromy of Frobenius solutions of differential equations arising in algebraic geometry. We represent Frobenius constants related to families of elliptic curves…

This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.

The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this…

We prove that the Connes embedding problem is stable under graph products.

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…