Related papers: Notes on Frobenius stable direct images

We study second order and third order linear differential equations with analytic coefficients under the viewpoint of finding formal solutions and studying their convergence. We address some untouched aspects of Frobenius methods for second…

A VI-module gives rise to a sequence of representations of the finite general linear groups. We prove that the sequence obtained from any finitely generated VI-module over an algebraically closed field of characteristic zero is…

We continue the development of $\mathbb{Z}^n_2$-supergeometry, a natural generalization of classical ($\mathbb{Z}_2$-graded) supergeometry, by proving the Frobenius theorem for integrable distributions on differentiable…

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

This paper aims to investigate effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sub-linear system $|S^0_{-}(X, K_X + nK_X)| \subseteq |H^0(X, K_X…

We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…

Owing to the difference in $K$-theory, an example by Dugger and Shipley implies that the equivalence of stable categories of Gorenstein projective modules should not be a Quillen equivalence. We give a sufficient and necessary condition for…

In Part I, we use Steenrod's construction to prove that the quantum Coulomb branch is a Frobenius-constant quantization. We will also demonstrate the corresponding result for the $K$-theoretic version of the quantum Coulomb branch. In Part…

Let $A$ be a non-CM simple abelian variety over a number field $K$. For a place $v$ of $K$ such that $A$ has good reduction at $v$, let $F(A,v)$ denote the Frobenius field generated by the corresponding Frobenius eigenvalues. Assuming $A$…

We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework.…

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…

We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As…

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…

Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…

We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.

We give a short new proof of a version of the Kruskal-Katona theorem due to Lov\'asz. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a…

We give a shorter proof to a recent result by Neuberger, in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results presented in Neuberger.

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…