Related papers: Adams operations on higher arithmetic K-theory
We show that the Adams operations in complex K-theory lift to operations in smooth K-theory. The main result is a Riemann-Roch type theorem about the compatibility of the Adams operations and the integration in smooth K-theory.
We introduce a new morphism between algebraic and hermitian K-theory. The topological analog is the Adams operation in real K-theory. From this morphism, we deduce a lower bound for the higher algebraic K-theory of a ring A in terms of the…
For any regular noetherian scheme X and every k>0, we define a chain morphism between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by the field of rational numbers. It…
In this paper we consider the K-theory of smooth algebraic stacks, establish lambda and gamma operations, and show that the higher K-theory of such stacks is always a pre-lambda-ring, and is a lambda-ring if every coherent sheaf is the…
We define quantum deformations of Adams operations in $K$-theory, in the framework of quasimap quantum $K$-theory. They provide $K$-theoretic analogs of the quantum Steenrod operations from equivariant symplectic Gromov--Witten theory. We…
We study a collection of operations on the cohomotopy of any space, with which it becomes a "beta-ring", an algebraic structure analogous to a lambda-ring. In particular, this ring possesses Adams operations, represented by maps on the…
Adams operations are the natural transformations of the representation ring functor on the category of finite groups, and they are one way to describe the usual lambda-ring structure on these rings. From the representation-theoretical point…
We construct a family of additive endomorphisms $\Psi_k, k=1, 2...$ of the Grothendieck ring of quasiprojective varieties and the Grothendieck ring of Chow motives similar to the Adams operations in the K-theory. The speciality of the…
We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the…
We describe explicitly the algebras of degree zero operations in connective and periodic p-local complex K-theory. Operations are written uniquely in terms of certain infinite linear combinations of Adams operations, and we give formulas…
The theory of secondary chomology operations leads to a conjecture concerning the algebra of higher cohomology operations in general. This conjecture is discussed here in detail and its connection with homotopy groups of spheres and the…
We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory, which includes all group morphisms. In…
We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the respective periodic spectra. The…
In this paper, extending the results in \cite{F}, we compute Adams operations on twisted $K$-theory of connected, simply-connected and simple compact Lie groups $G$, in both equivariant and nonequivariant settings.
The $C_2$-spectrum of Atiyah's Real $K$-theory is denoted by $\mathbf{KR}$ and the $C_2$-spectrum of topological modular forms of level structure $\Gamma_1(3)$ by $\mathbf{TMF}_1(3)$. In this short note we compute the $C_2$-equivariant…
We investigate the relations between the Grothendieck group of coherent modules of an algebraic variety and its Chow group of algebraic cycles modulo rational equivalence. Those are in essence torsion phenomena, which we attempt to control…
Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…
This paper proves that the homotopy type of a pointed, simply-connected, 2-reduced simplicial set is determined by the chain-complex augmented by functorial diagonal and higher diagonal maps (a simple generalization of the ones used to…
We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents…
The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a…