Related papers: Notes on Frobenius stable direct images

We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations.…

This article concerns properties of mixed $\ell$-adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism. We establish a fiberwise criterion for the semisimplicity and Frobenius semisimplicity of…

We prove that any faithful Frobenius functor between abelian categories preserves the Gorenstein projective dimension of objects. Consequently, it preserves and reflects Gorenstein projective objects. We give conditions on when a Frobenius…

We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety by a finite group of order prime to the…

This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008, Seoul. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius…

We study the homotopy fixed points under the Frobenius endomorphism on the stable $\mathbb A^1$-homotopy category of schemes in characteristic $p>0$ and prove a rigidity result for cellular objects in these categories after inverting $p$.…

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be…

Let $k$ be a perfect field of characteristic $p >0$, $U$ be a variety over $k$ and $F$ be a power of Frobenius. We construct the category of overholonomic arithmetical ($F$-)$\D$-modules over $U$ and the category of overholonomic…

We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenstein projective objects. As such, the associated stable…

We present an example of a homogeneous projective variety the Frobenius direct image of the structure sheaf of which has nonvanishing self extension.

Up to a translation in the language of arithmetic $\D$-modules, we prove a conjecture of Berthelot on the preservation of the overconvergence under the direct image by a smooth proper morphism of varieties over a perfect field of…

We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $\nu$-dominant dimensions…

In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to…

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a toric fibration over…

We define the big crystalline site for a log scheme and prove the basic properties. In particular, we show the boundedness, base change, and perfectness theorems for the crystalline higher direct image of quasi-coherent crystals between…

In this work, the author gives a character-free proof of the Frobenius theorem. The new proof is based on some notions and results from the theory of ternary operations, the theory of orthogonal binary operations, the theory of transversals…

By using Christol and Mebkhout's algebrization and finiteness theorem, we prove that in the case of smooth curves, Berthelot's strongest conjecture on the stability of holonomicity is still valid without Frobenius structure but under some…

Let $X$ be a smooth projective surface over an algebraically closed field $k$ of characteristic $p> 0$ with $\Omega_{X}^{1}$ semistable and $\mu(\Omega_{X}^{1})>0$. For any semistable (resp. stable) bundle $W$ of rank $r$, we prove that…

We investigate the injectivity of the Frobenius map on thickenings of smooth varieties in projective space over a field of positive characteristic. We obtain uniform bounds -- i.e., independent of the characteristic -- on the thickening…

A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity…