Related papers: The Tate Intermediate Value Theorem
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We study the topological spectrum of a seminormed ring $R$ which we define as the space of prime ideals $\mathfrak{p}$ such that $\mathfrak{p}$ equals the kernel of some bounded power-multiplicative seminorm. For any seminormed ring $R$ we…
We evaluate the squeezing of a probe beam with a transverse Gaussian profile interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and…
We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
We explain the relationship between the classical description of an integrable system in terms of invariant tori and action-angle variables, and the quantum description in terms of the asymptotic Bethe ansatz.
Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…
Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…
Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…
Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$.…
In this talk we discuss enveloping algebra based noncommutative gauge field theory, constructed at the first order in noncommutative parameter theta, as an effective, anomaly free theory, with one-loop renormalizable gauge sector. Limits on…
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg…
We consider the derived category of permutation modules over a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the set underlying the tt-spectrum of compact…
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…
For any essentially small triangulated category the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for…
We study the variation of the Tait number of a closed space curve according to its different projections. The results are used to compute the writhe of a knot, leading to a closed formula in case of polygonal curves.
We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
We present a construction that manufactures $\E_\infty$ orientations of Tate fixed-point objects together with useful formulas for these maps, and then give a number of applications. For example, we produce a formula for the Frobenius…
We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their rings of continuous functions.