Related papers: Harder-Narasimhan theory
We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues. We prove the tensor product theorem, i.e., that the tensor product of semi-stable objects is again…
We define and study Harder-Narasimhan filtrations on Breuil-Kisin-Fargues modules and related objects relevant to p-adic Hodge theory.
We propose a generalization of Quillen's exact category -- arithmetic exact category and we discuss conditions on such categories under which one can establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan polygons.…
An axiomatisation of Hurkens's paradox in dependent type theory is given without assuming any impredicative feature of said type theory.
The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…
This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.
In a recent paper, Nagata [1] claims to derive inconsistencies from quantum mechanics. In this paper, we show that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables.
We prove a Kotake-Narasimhan type theorem in general ultradifferentiable classes given by weight matrices. In doing so we simultaneously recover and partially generalize the known results for classes given by weight sequences and weight…
We establish in this article convergence results of normalized Harder-Narasimhan polygons both in geometric and in arithmetic frameworks by introducing the Harder-Narasimhan filtration indexed by $\mathbb R$ and the associated Borel…
It is argued that the massive gauge field theory without the Higgs mechanism can well be set up on the gauge-invariance principle based on the viewpoint that a massive gauge field must be viewed as a constrained system and the Lorentz…
We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.
In this article, we study the notion of semi-stability and the Harder-Narasimhan filtration from a game-theoretic point of view. This allows us to provide a unified proof for the existence and uniqueness of the Harder-Narasimhan filtration…
Starting from our work on Harder-Narasimhan filtrations of finite flat group schemes over a $p$-adic field, we developp a theory of Harder-Narasimhan filtrations for $p$-divisible groups. We apply this to the study of the geometry of period…
We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
Raghavan Narasimhan outlined a new proof of L. Schwartz's perturbation theorem during a course of lectures at IMSc, Chennai in Spring 2007. The details are given.
A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.
A short and direct proof of the Gibbard-Satterthwaite theorem \`{a} la Amartya Sen's proof of Arrow's impossibility theorem is given.
We give a simple proof of a general theorem of Kotake-Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based on an example of…
In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.