We study the existence of a Batalin-Vilkovisky differential on complete cohomology ring Frobenius algebra. construct in case algebras with diagonalizable Nakayama automorphisms.

The moduli space of principally polarized abelian varieties $A_g$ genus g is defined over the integers and admits a minimal compactification $A_g^*$, also integers. Hodge bundle has its Chern classes in Chow ring with rational coefficients. We show that prime field $F_p$, these naturally lift to $A_g^*$ do so best possible way: despite highly singular nature they are represented by algebraic cy...

This preprint contains proofs of the results anounced in [PS] in the part concerning the construction of push-forwards for an oriented cohomology theory. It is constructed one-to-one correspondences between orientations, Chern structures, Thom structures and integrations on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism t...

LetG be a reductive linear algebraic group over a field k. LetA be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that the ring of invariantsA = H 0(G,A) is finitely generated. We show that in fact the full cohomology ringH ∗(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology cla...

We show that Sullivan's model of rational differential forms on a simplicial set X may be interpreted as (kind of) 0 | 1 -dimensional supersymmetric quantum field theory over , and, consequence, concordance classes such theories represent the cohomology . introduce notion superalgebraic cartesian sets concept space which should roughly thought blend and supermanifolds, but valid an arbitrary ba...

We define the cohomological Burnside ring B(G,M) of a finite group G with coefficients in a ZG-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X(G,M). The cohomology groups H ∗ X(G,M) are defined in such a way that H∗ X(G, M) ∼= ⊕iH∗(Hi,M) when X is the disjoint union of transitive G-sets G/Hi. I...

Answering a question of W. S. Wilson, I introduce a Z/2equivariant Atiyah-Real analogue of Johnson-Wilson cohomology theory BP 〈n〉, whose coefficient ring is the ≤ n-chromatic part of Landweber’s Real cobordism ring. AMS Classification 55P42, 55P91; 55T25

Let F be a real quadratic field with ring of integers Ø and with class number 1. Let Γ be a congruence subgroup of GL2(Ø). We describe a technique to compute the action of the Hecke operators on the cohomology H(Γ ;C). For F real quadratic this cohomology group contains the cuspidal cohomology corresponding to cuspidal Hilbert modular forms of parallel weight 2. Hence this technique gives a way...

This preprint contains proofs of the results anounced in PS] in the part concerning the construction of push-forwards for an oriented cohomology theory. One-to-one correspondences are constructed between orientations, Chern structures, Thom structures and integrations on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theo...

This is a survey paper on cohomology theories for A∞ and E∞ ring spectra. Different constructions and main properties of topological André-Quillen cohomology and of topological derivations are described. We give sample calculations of these cohomology theories and outline applications to the existence of A∞ and E∞ structures on various spectra. We also explain the relationship between topologic...