Transfer and complex oriented cohomology rings

Cohomology Rings and Nilpotent Quotients of Real and Complex Arrangements

For an arrangement with complement X and fundamental group G, we relate the truncated cohomology ring, H≤2(X), to the second nilpotent quotient, G/G3. We define invariants of G/G3 by counting normal subgroups of a fixed prime index p, according to their abelianization. We show how to compute this distribution from the resonance varieties of the Orlik-Solomon algebra mod p. As an application, we...

THE TANGENT COMPLEX AND HOCHSCHILD COHOMOLOGY OF En-RINGS

In this work, we study the deformation theory of En-rings and the En analogue of the tangent complex, or topological André-Quillen cohomology. We prove a generalization of a conjecture of Kontsevich, that there is a fiber sequence A[n − 1] → TA → HHEn (A)[n], relating the En-tangent complex and En-Hochschild cohomology of an En-ring A. We give two proofs: The first is direct, reducing the probl...

Cohomology of Λ-rings

A cohomology theory for λ-rings is developed. This is then applied to study deformations of λ-rings.

Fontaine Rings and Local Cohomology

1. Introduction In this paper we use Fontaine rings to study properties of local cohomology for rings of mixed characteristic. Fontaine rings, which we deene and discuss in more detail in Section 3, give a method of constructing a ring of positive characteristic from one of mixed characteristic in such a way that,

Cohomology rings of arrangements