Related papers: Equivariant Fixed Point Theory
Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…
In this paper, for a finite group, we discuss a method for calculating equivariant homology with constant coefficients. We apply it to completely calculate the geometric fixed points of the equivariant spectrum representing equivariant…
We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.
We prove a general inequality for estimating the number of points of arbitrary complete intersections over a finite field. This extends a result of Deligne for nonsingular complete intersections. For normal complete intersections, this…
We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…
We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…
In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…
We prove a version of Grothendieck's descent theorem on an `enriched' principal fiber bundle, a principal fiber bundle with an action of a larger group scheme. Using this, we prove the isomorphisms of the equivariant Picard and the class…
We extend Milnor's mu-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
In this article, we suggest a categorification procedure in order to capture an analogy between Crystalline Grothendieck-Lefschetz trace formula and the cyclotomic trace map $K\rightarrow TC$ from the algebraic $K$-theory to the topological…
In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…
The additivity of traces in certain tensor triangulated categories for endomorphisms of finite order of distinguished triangles is investigated. For the identity endomorphism this has been fully established by J. P. May ("The additivity of…
We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…
In this article, we discuss the Lefschetz trace formula for an adic space which is separated smooth of finite type but not necessarily proper over an algebraically closed non-archimedean field. Under a certain condition on the absence of…
This note is concerned with isometries on the spaces of self-adjoint traceless matrices. We compute the group of isometries with respect to any unitary similarity invariant norm. This completes and extends the result of Nagy on Schatten…
We prove a cyclic Lefschetz formula for foliations. To this end, we define a notion of equivariant cyclic cohomology and show that its expected pairing with K-theory is well defined. This enables to associate to any invariant transverse…
In the present paper, we discuss applications of the derived completion theorems proven in our previous two papers. One of the main applications is to Riemann-Roch problems for forms of higher equivariant K-theory, which we are able to…
We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…