This paper is the second one in a series of papers about operations in motivic cohomology. Here we show that in the context of smooth schemes over a field of characteristic zero all the bi-stable operations can be obtained in the usual way from the motivic reduced powers and the Bockstein homomorphism (Theorem 4.46). This paper has been delayed for many years because I tried to find a way to ex...

Floer cohomology groups are usually defined over a field of formal functions (a Novikov field). Under certain assumptions, one can equip them with connections, which means operations differentiation respect to the variable. This allows write differential equations for classes. Here, we apply that idea symplectic associated Lefschetz fibrations, and establish relation enumerative geometry.

The close relationship between the scheme of level structures on universal deformation a formal group and Morava E-cohomology finite abelian groups has played an important role in study power operations for E-theory. goal this paper is to explore p-divisible given by trivial extension constant iterated free loop space classifying group.

The mod 2 Steenrod algebra A and Dyer-Lashof algebra R have both striking similarities and differences, arising from their common origins in “lower-indexed” algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra K, whose module actions are equivalent to, but quite different from, those of A and R. The exact relationships emerge as “sheared algebra bij...

We give a brief introduction to the study of the algebraic structures – and their geometrical interpretations – which arise in the BRST construction of a conformal string background. Starting from the chiral algebra A of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson struct...

In this paper we consider the K-theory of smooth algebraic stacks, establish λ and Adams operations and show that the higher K-theory of such stacks is always a pre-λ-ring and is a λ-ring if every coherent sheaf is the quotient of a vector bundle. As a consequence we are able to define Adams operations and absolute cohomology for smooth algebraic stacks satisfying this hypothesis. We also defin...

let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...