Related papers: Equivariant Fixed Point Theory
We show that an important classical fixed point invariant, the Reidemeister trace, arises as a topological Hochschild homology transfer. This generalizes a corresponding classical result for the Euler characteristic and is a first step in…
In this article, we introduce and develop the notion of parametrised Poincar\'{e} duality in the formalism of parametrised higher category theory by Martini-Wolf, in part generalising Cnossen's theory of twisted ambidexterity to the…
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…
We give an alternative treatment of the foundations of parametrized spectra, with an eye toward applications in fixed-point theory. We cover most of the central results from the book of May and Sigurdsson, sometimes with weaker hypotheses,…
In this paper, we define the notion of graph trace kernels as a generalization of trace kernels. We associate a microlocal Lefschetz class with a graph trace kernel and prove that this class is functorial with respect to the composition of…
We establish the invariant trace formula (\`a la Arthur) for the ad\'elic covers of connected reductive groups over a number field, under the hypothesis that the trace Paley-Wiener theorem is verified for all Levi subgroups at the real…
Using the language of stacks, we recast and generalize a selection of results in equivariant geometry.
We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K_0 of the category of "phi-endomorphisms of finitely generated free…
We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and…
In this article, we consider regular projective arithmetic schemes in the context of Arakelov geometry, any of which is endowed with an action of the diagonalisable group scheme associated to a finite cyclic group and with an equivariant…
We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.
We use the formalism of traces in higher categories to prove a common generalization of the holomorphic Atiyah-Bott fixed point formula and the Grothendieck-Riemann-Roch theorem. The proof is quite different from the original one proposed…
Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization…
In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary.
This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we…
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
We develop a new approach to the pulling back fixed point theorem of W. Browder and use it in order to prove various generalizations of this result.
We give a simple criterion so that a countable infinite direct sum of trace (evaluation) maps is a trace map. An application to the theory of self-adjoint extensions of direct sums of symmetric operators is provided; this gives an…
In the past decades, one of the most fruitful approaches to the study of algebraic $K$-theory has been trace methods, which construct and study trace maps from algebraic $K$-theory to topological Hochschild homology and related invariants.…