Cohomology of tails and stable cohomology over Koszul quiver algebras

2005 ◽  
pp. 299-306
Author(s):  
Roberto Martínez Villa ◽  
Alex Martsinkovsky
Keyword(s):  
Stable Cohomology

scholarly journals An Infinite Genus Mapping Class Group and Stable Cohomology

2009 ◽  
Vol 287 (3) ◽  
pp. 787-804 ◽  
Author(s):  
Louis Funar ◽  
Christophe Kapoudjian
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Stable Cohomology

scholarly journals Goresky–Pardon lifts of Chern classes and associated Tate extensions

2017 ◽  
Vol 153 (7) ◽  
pp. 1349-1371 ◽  
Author(s):  
Eduard Looijenga
Keyword(s):  
Vector Bundle ◽  
Hodge Structure ◽  
Holomorphic Vector Bundle ◽  
Mixed Hodge Structure ◽  
Chern Classes ◽  
Analytic Variety ◽  
Algebraic Setting ◽  
Geometric Conditions ◽  
Stable Cohomology ◽  
Complex Analytic Variety

Let $X$ be an irreducible complex-analytic variety, ${\mathcal{S}}$ a stratification of $X$ and ${\mathcal{F}}$ a holomorphic vector bundle on the open stratum ${X\unicode[STIX]{x0030A}}$. We give geometric conditions on ${\mathcal{S}}$ and ${\mathcal{F}}$ that produce a natural lift of the Chern class $\operatorname{c}_{k}({\mathcal{F}})\in H^{2k}({X\unicode[STIX]{x0030A}};\mathbb{C})$ to $H^{2k}(X;\mathbb{C})$, which, in the algebraic setting, is of Hodge level ${\geqslant}k$. When applied to the Baily–Borel compactification $X$ of a locally symmetric variety ${X\unicode[STIX]{x0030A}}$ and an automorphic vector bundle ${\mathcal{F}}$ on ${X\unicode[STIX]{x0030A}}$, this refines a theorem of Goresky–Pardon. In passing we define a class of simplicial resolutions of the Baily–Borel compactification that can be used to define its mixed Hodge structure. We use this to show that the stable cohomology of the Satake ($=$ Baily–Borel) compactification of ${\mathcal{A}}_{g}$ contains nontrivial Tate extensions.

scholarly journals The stable cohomology of the Satake compactification of 𝒜g

2017 ◽  
Vol 21 (4) ◽  
pp. 2231-2241 ◽  
Author(s):  
Jiaming Chen ◽  
Eduard Looijenga
Keyword(s):  
Stable Cohomology

Cohomology operations and duality

1968 ◽  
Vol 64 (1) ◽  
pp. 15-30 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Vector Spaces ◽  
Kronecker Products ◽  
Dual Vector ◽  
Alexander Duality ◽  
Cohomology Operation ◽  
Yield Information ◽  
Stable Cohomology ◽  
Steenrod Square ◽  
Cohomology Operations ◽  
Image Position

Since Thom first introduced the notion of the ‘dual’ of a Steenrod square, in (12), it has become apparent that calculation with such duals in the cohomology of, say, a simplicial complex X will often yield information about the impossibility of embedding X in Sn, for certain values of n. For example, the celebrated theorem that cannot be embedded in can easily be proved in this way. In this paper, we seek to generalize this method to any pair of extraordinary cohomology theories h* and k*, and natural stable cohomology operation θ: h* → k*. We show in section 3 that a simplicial embeddingf: X → Sn gives rise via the Alexander duality isomorphism to a homology operationwhich is independent of n, the particular embedding f, and even the particular triangulations of X and Sn. If h* and k* are multiplicative cohomology theories, there are Kronecker productsif h0(S0) = k0(S0) = G, a field, and the Kronecker products make h*, h* and k*, k* into dual vector spaces over G, then can be turned into a cohomology operation c(θ): k*(X)→h*(X), by using this duality. This is certainly true if h* = k* = H*(;Zp), p prime, and in this case we have the original situation considered by Thom, who showed, for example, that

The Relation Between Stable Operations for Connective and Non-Connective p-Local Complex K-Theory

1986 ◽  
Vol 29 (2) ◽  
pp. 246-255 ◽  
Author(s):  
Keith Johnson
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Local Complex ◽  
Stable Cohomology ◽  
Cohomology Operations ◽  
K Theory ◽  
Necessary And Sufficient

AbstractThe question of which degree 0 stable cohomology operations for connective K-theory localized at a prime p arise from operations for non-connective K-theory is investigated. A necessary and sufficient condition is established, and an example of a connective operation not arising in this way is constructed.

scholarly journals Stable cohomology of the perfect cone toroidal compactification of 𝒜 g

2018 ◽  
Vol 2018 (741) ◽  
pp. 211-254 ◽  
Author(s):  
Samuel Grushevsky ◽  
Klaus Hulek ◽  
Orsola Tommasi
Keyword(s):  
Moduli Space ◽  
Polynomial Algebra ◽  
Abelian Varieties ◽  
Fixed Degree ◽  
Toroidal Compactifications ◽  
Stable Cohomology

Abstract We show that the cohomology of the perfect cone (also called first Voronoi) toroidal compactification {{{\mathcal{A}}_{g}^{\operatorname{Perf}}}} of the moduli space of complex principally polarized abelian varieties stabilizes in close to the top degree. Moreover, we show that this stable cohomology is purely algebraic, and we compute it in degree up to 13. Our explicit computations and stabilization results apply in greater generality to various toroidal compactifications and partial compactifications, and in particular we show that the cohomology of the matroidal partial compactification {{{\mathcal{A}}_{g}^{\operatorname{Matr}}}} stabilizes in fixed degree, and forms a polynomial algebra. For degree up to 8, we describe explicitly the generators of the cohomology, and discuss various approaches to computing all of the stable cohomology in general.

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