scholarly journals Support varieties over skew complete intersections via derived braided Hochschild cohomology

2021 ◽  
Author(s):  
Luigi Ferraro ◽  
W. Frank Moore ◽  
Josh Pollitz
Keyword(s):  
Hochschild Cohomology ◽  
Complete Intersections ◽  
Support Varieties

scholarly journals A Spectral Sequence for the Hochschild Cohomology of a Coconnective DGA

2013 ◽  
Vol 112 (2) ◽  
pp. 182 ◽  
Author(s):  
Shoham Shamir
Keyword(s):  
Spectral Sequence ◽  
Loop Space ◽  
Hochschild Cohomology ◽  
Derived Category ◽  
Orientable Manifold ◽  
Support Varieties ◽  
Mod P

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence presented in [7] for the computation of the loop homology of a closed orientable manifold. Using this spectral sequence we identify a class of spaces for which the Hochschild cohomology of their mod-$p$ cochain algebra is Noetherian. This implies, among other things, that for such a space the derived category of mod-$p$ chains on its loop-space carries a theory of support varieties.

scholarly journals THE HOCHSCHILD COHOMOLOGY RING OF A CLASS OF SPECIAL BISERIAL ALGEBRAS

2010 ◽  
Vol 09 (01) ◽  
pp. 73-122 ◽  
Author(s):  
NICOLE SNASHALL ◽  
RACHEL TAILLEFER
Keyword(s):  
London Math ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Krull Dimension ◽  
Finitely Generated ◽  
Cohomology Rings ◽  
Hochschild Cohomology Ring ◽  
Special Biserial Algebras ◽  
Support Varieties

We consider a class of self-injective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of dΛN is a finitely generated K-algebra. Moreover, the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative K-algebra of Krull dimension two. As a consequence the conjecture of [N. Snashall and Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc.88 (2004) 705–732], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.

scholarly journals Support varieties and cohomology over complete intersections

2000 ◽  
Vol 142 (2) ◽  
pp. 285-318 ◽  
Author(s):  
Luchezar L. Avramov ◽  
Ragnar-Olaf Buchweitz
Keyword(s):  
Complete Intersections ◽  
Support Varieties

scholarly journals Hochschild cohomology of some quantum complete intersections

2018 ◽  
Vol 17 (11) ◽  
pp. 1850215 ◽  
Author(s):  
Karin Erdmann ◽  
Magnus Hellstrøm-Finnsen
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Complete Intersections ◽  
Root Of Unity ◽  
Nilpotent Elements ◽  
Hochschild Cohomology Ring ◽  
Quantum Complete Intersections ◽  
Primitive Formula

We compute the Hochschild cohomology ring of the algebras [Formula: see text] over a field [Formula: see text] where [Formula: see text] and where [Formula: see text] is a primitive [Formula: see text]th root of unity. We find the dimension of [Formula: see text] and show that it is independent of [Formula: see text]. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

scholarly journals Support varieties and Hochschild cohomology rings

2004 ◽  
Vol 88 (03) ◽  
pp. 705-732 ◽  
Author(s):  
Nicole Snashall ◽  
Øyvind Solberg
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Rings ◽  
Support Varieties

scholarly journals HOCHSCHILD COHOMOLOGY AND SUPPORT VARIETIES FOR TAME HECKE ALGEBRAS

2010 ◽  
Vol 62 (4) ◽  
pp. 1017-1029 ◽  
Author(s):  
S. Schroll ◽  
N. Snashall
Keyword(s):  
Hochschild Cohomology ◽  
Hecke Algebras ◽  
Support Varieties

scholarly journals The Hochschild cohomology of square-free monomial complete intersections

2019 ◽  
Vol 47 (8) ◽  
pp. 3040-3055 ◽  
Author(s):  
Nghia T. H. Tran ◽  
Emil Sköldberg
Keyword(s):  
Hochschild Cohomology ◽  
Complete Intersections

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

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