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Displaying similar documents to “Chen–Ruan Cohomology of 1 , n and ¯ 1 , n

Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

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Let  G be a split semisimple linear algebraic group over a field and let  T be a split maximal torus of  G . Let  𝗁 be an oriented cohomology (algebraic cobordism, connective K -theory, Chow groups, Grothendieck’s K 0 , etc.) with formal group law F . We construct a ring from F and the characters of  T , that we call a formal group ring, and we define a characteristic ring morphism c from this formal group ring to  𝗁 ( G / B ) where G / B is the variety of Borel subgroups of  G . Our main result says that when the...

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

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We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles...

On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals

Thiago H. Freitas, Victor H. Jorge Pérez (2019)

Czechoslovak Mathematical Journal

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Let 𝔞 , I , J be ideals of a Noetherian local ring ( R , 𝔪 , k ) . Let M and N be finitely generated R -modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of H I , J t ( M ) and D ( H I , J t ( M ) ) , where t is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and D ( - ) : = Hom R ( - , E R ( k ) ) is the Matlis dual functor. We show that if R is a d -dimensional complete Cohen-Macaulay...

S -depth on Z D -modules and local cohomology

Morteza Lotfi Parsa (2021)

Czechoslovak Mathematical Journal

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Let R be a Noetherian ring, and I and J be two ideals of R . Let S be a Serre subcategory of the category of R -modules satisfying the condition C I and M be a Z D -module. As a generalization of the S - depth ( I , M ) and depth ( I , J , M ) , the S - depth of ( I , J ) on M is defined as S - depth ( I , J , M ) = inf { S - depth ( 𝔞 , M ) : 𝔞 W ˜ ( I , J ) } , and some properties of this concept are investigated. The relations between S - depth ( I , J , M ) and H I , J i ( M ) are studied, and it is proved that S - depth ( I , J , M ) = inf { i : H I , J i ( M ) S } , where S is a Serre subcategory closed under taking injective hulls. Some conditions are provided that local cohomology...

Matlis dual of local cohomology modules

Batoul Naal, Kazem Khashyarmanesh (2020)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a commutative Noetherian local ring, 𝔞 be an ideal of R and M a finitely generated R -module such that 𝔞 M M and cd ( 𝔞 , M ) - grade ( 𝔞 , M ) 1 , where cd ( 𝔞 , M ) is the cohomological dimension of M with respect to 𝔞 and grade ( 𝔞 , M ) is the M -grade of 𝔞 . Let D ( - ) : = Hom R ( - , E ) be the Matlis dual functor, where E : = E ( R / 𝔪 ) is the injective hull of the residue field R / 𝔪 . We show that there exists the following long exact sequence 0 H 𝔞 n - 2 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n ( D ( H 𝔞 n ( M ) ) ) D ( M ) H 𝔞 n - 1 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n + 1 ( D ( H 𝔞 n ( M ) ) ) H 𝔞 n ( D ( H ( x 1 , ... , x n - 1 ) n - 1 ( M ) ) ) H 𝔞 n ( D ( H ( n - 1 M ) ) ) ... , where n : = cd ( 𝔞 , M ) is a non-negative integer, x 1 , ... , x n - 1 is a regular sequence in 𝔞 on M and, for an R -module L , H 𝔞 i ( L ) is the i th local cohomology module...

An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel (2014)

Journal de Théorie des Nombres de Bordeaux

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Let C be a hyperelliptic curve of genus g 1 over a number field K with good reduction outside a finite set of places S of K . We prove that C has a Weierstrass model over the ring of integers of K with height effectively bounded only in terms of g , S and K . In particular, we obtain that for any given number field K , finite set of places S of K and integer g 1 one can in principle determine the set of K -isomorphism classes of hyperelliptic curves over K of genus g with good reduction outside...

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

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Let R and S be commutative rings with unity, f : R S a ring homomorphism and J an ideal of S . Then the subring R f J : = { ( a , f ( a ) + j ) a R and j J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R f J is a (generalized) filter ring.

Cofiniteness and finiteness of local cohomology modules over regular local rings

Jafar A'zami, Naser Pourreza (2017)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss R ( R / I ) = Assh R ( I ) . It is shown that the R -module H I ht ( I ) ( R ) is I -cofinite if and only if cd ( I , R ) = ht ( I ) . Also we present a sufficient condition under which this condition the R -module H I i ( R ) is finitely generated if and only if it vanishes.

Multiple end solutions to the Allen-Cahn equation in 2

Michał Kowalczyk, Yong Liu, Frank Pacard (2013-2014)

Séminaire Laurent Schwartz — EDP et applications

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An entire solution of the Allen-Cahn equation Δ u = f ( u ) , where f is an odd function and has exactly three zeros at ± 1 and 0 , e.g. f ( u ) = u ( u 2 - 1 ) , is called a 2 k end solution if its nodal set is asymptotic to 2 k half lines, and if along each of these half lines the function u looks (up to a multiplication by - 1 ) like the one dimensional, odd, heteroclinic solution H , of H ' ' = f ( H ) . In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space...

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

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Let M be any compact simply-connected oriented d -dimensional smooth manifold and let 𝔽 be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of M , H H * ( S * ( M ) , S * ( M ) ) , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on M , H * + d ( L M ) introduced by Chas and Sullivan. We also show that the negative cyclic...

The clean elements of the ring ( L )

Ali Akbar Estaji, Maryam Taha (2024)

Czechoslovak Mathematical Journal

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We characterize clean elements of ( L ) and show that α ( L ) is clean if and only if there exists a clopen sublocale U in L such that 𝔠 L ( coz ( α - 1 ) ) U 𝔬 L ( coz ( α ) ) . Also, we prove that ( L ) is clean if and only if ( L ) has a clean prime ideal. Then, according to the results about ( L ) , we immediately get results about 𝒞 c ( L ) .

On extending C k functions from an open set to with applications

Walter D. Burgess, Robert M. Raphael (2023)

Czechoslovak Mathematical Journal

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For k { } and U open in , let C k ( U ) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f C k ( U ) there is g C ( ) with U coz g and h C k ( ) with f g | U = h | U . The function f and its k derivatives are not assumed to be bounded on U . The function g is constructed using splines based on the Mollifier function. Some consequences about the ring C k ( ) are deduced from this, in particular that Q cl ( C k ( ) ) = Q ( C k ( ) ) .