Related papers: Harder-Narasimhan theory

In this paper we prove the theorem on freedom for relatively free Lie algebras with a single relation (analogous with the well-known result of Shirshov) and a generalized Freiheitssatz for relatively free Lie algebras (analogous with the…

We formulate Aubry-Mather theory for Hamiltonians/Lagrangians defined on graphs and discuss its relationship with weak KAM theory developed in [24].

We revisit the Harder-Narasimhan stratification on a minuscule $p$-adic flag variety, by the theory of modifications of $G$-bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan strata with the Newton strata introduced by…

We build on the recent techniques of Codogni and Patakfalvi, from \cite{Codogni:Patakfalvi:2021}, which were used to establish theorems about semi-positivity of the Chow Mumford line bundles for families of $\K$-semistable Fano varieties.…

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

We look at various questions related to filtrations in $p$-adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of…

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

This article is a thorough critique to the Plakhutin-Davidson's comments made to our paper published in the recent year. A detailed critical examination of the arguments that led to the suggested comments by Plakhutin and Davidson reveals…

In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…

Take a holomorphic Lie algebroid $(V,\, \phi)$ on a compact connected Riemann surface $X$ such that the anchor map $\phi$ is not surjective. Let $P$ be a parabolic subgroup of a complex reductive affine algebraic group $G$ and $E_P\,…

In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose…

We analyze the consistency of the Chiral Lagrangian approach to the description of the spin 3/2 interacting theory. We argue that to lowest order in the 1/m expansion, the formalism leads to the appropriated constraints and the theory is…

We give a simple diagrammatic proof of the Frobenius property for generic fibrations, that does not depend on any additional structure on the interval object such as connections.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

This paper deals with a question of Fontaine and Rapoport which was posed in math.NT/0204293. There they asked for the determination of the index set of the Harder-Narasimhan vectors of the filtered isocrystals with fixed Newton- and Hodge…

The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of…

In this paper, we establish the parahoric reduction theory of formal connections (or Higgs fields) on a formal principal bundle with parahoric structures, which generalizes Babbitt-Varadarajan's result for the case without parahoric…

In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.

In the paper it is demonstrated that Bells theorem is an unprovable theorem.