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We give a presentation for the cohomology algebra of the Spaltenstein variety of all partial flags annihilated by a fixed nilpotent matrix, generalizing the description of the cohomology algebra of th...
Rational cohomology of \bar R_2 (and \bar S_2)
Rational cohomology \bar R_2 (and \bar S_2)
2011/2/25
In this text we compute the rational cohomology ring of R2, the moduli space of Prym curves of genus 2, which is, as we also show, isomorphic to the rational Chow ring of this space. G. Bini and C.
Quantum cohomology of the odd symplectic Grassmannian of lines
Quantum cohomology odd symplectic Grassmannian of lines
2011/2/23
Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of line...
In this paper we construct a graded Lie algebra on the space of cochains on a Z2-graded vector space V = V0 ⊕ V1 that are skew-symmetric on the subspace V1. The Lie bracket is obtained from the classi...
Cohomology and L-values
Cohomology L-values
2011/2/24
In a paper published in 1959, Shimura presented an elegant calcu-lation of the critical values of L-functions attached to elliptic modular forms using the first cohomology group. We will show that a s...
Cusp form motives in the cohomology of the space of stable maps to BG
motives cohomology of the space stable maps
2011/1/19
The moduli space M1,n(B(Z/mZ)2) of twisted stable maps into the stack B(Z/mZ)2 carries a natural Sn-action and so its cohomology may be decomposed into irreducible Sn-representations.
A cohomological obstruction to weak approximation for homogeneous spaces
Brauer-Manin obstruction weak approximation homogeneous spaces
2011/1/19
Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H G is a k-subgroup (not necessarily con-nected). Let S be a finite set of places of k...
The stable cohomology of automorphisms of free groups with coefficients in the homology representation
Automorphisms of free groups homology stability
2011/1/19
We study the cohomology of Aut(F n) and Out(F n) with coeffi-cients in the modules ^qH, ^H, SymqH or SymqH, where H is the Out(F n)-module obtained by abelianising the free group F
n.
On the homological mirror symmetry conjecture for pairs of pants
homological mirror symmetry pairs of pants
2011/2/21
The n-dimensional pair of pants is defined to be the complement of n + 2 generic hyperplanes in CPn. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism A∞ alg...
A Giambelli formula for the $S^1$-equivariant cohomology of type A Peterson varieties
Giambelli formula $S^1$-equivariant cohomology of type Peterson varieties
2011/2/22
The main result of this note is a Giambelli formula for the Peterson Schubert classes in the S1-equivariant cohomology ring of a type A Peterson variety. Our results depend on the Monk formula for the...
Lie-Hopf algebras and their Hopf cyclic cohomology
Lie-Hopf algebras Hopf cyclic cohomology
2011/2/24
The correspondence between Lie algebras, Lie groups, and alge-braic groups, on one side and commutative Hopf algebras on the other side are known for a long time by works of Hochschild-Mostow and othe...
Residual d-bar-cohomology and the complex Radon transform on subvarieties of CPn
Residual d-bar-cohomology complex Radon transform subvarieties of CPn
2011/2/24
We show that the complex Radon transform realizes an isomorphism between the space of residual
¯ @-cohomologies of a locally complete intersection subvariety in a linearly concave domain of CPn ...
We show that for any block algebra B of a finite group over an algebraically closed field
of prime characteristic p the dimension of HHn(B) is bounded by a function depending only
on the nonnegative...
Deformation of locally free actions and the leafwise cohomology
Deformation of locally free actions leafwise cohomology
2011/1/21
This is a note of my lectures at “Advanced courses in Foliation” in the research program “Foliation”, which was held at the Centre de Recerca Mathem`atica in the May of 2010. In this note, we discuss ...
This paper introduces the notion of Arakelov motivic cohomology. We construct a ring spectrum HD representing Deligne cohomology which is shown to enjoy a unique algebra structure over the spectrum HB...