Related papers: Ghost classes in $\mathbb{Q}$-rank two orthogonal …

We study the asymptotic behaviour of the cohomology of subgroups $\Gamma$ of an algebraic group $G$ with coefficients in the various irreducible rational representations of $G$ and raise a conjecture about it. Namely, we expect that the…

We analyze the ghost issue in the recently proposed models of non-linear massive gravity in the ADM formalism. We show that, in the entire two-parameter family of actions, the Hamiltonian constraint is maintained at the complete non-linear…

Brasselet, the second author and Yokura introduced Hodge-theoretic Hirzebruch-type characteristic classes $IT_{1, \ast}$, and conjectured that they are equal to the Goresky-MacPherson $L$-classes for pure-dimensional compact complex…

In this paper, we construct models that admit the traversable wormhole geometries in the framework of Einstein's gravity with two scalar fields. As well known, the energy conditions are broken and we show that there appears a ghost. The…

Ghost modules were introduced in [I3] without definitions or proofs. We also introduced stability diagrams or "relative pictures" for torsion classes and torsion-free classes for representations of Dynkin quivers. Modules which were not in…

In this paper we establish the correspondence between ghost-free bimetric theory and a class of higher derivative gravity actions, including conformal gravity and New Massive Gravity. We also characterize the relation between the respective…

The number of ghost states at each energy level in a non-unitary conformal field theory is encoded in the signature characters of the relevant Virasoro algebra highest weight representations. We give expressions for these signature…

We present two new families of Abelian varieties which contradict Zarhin's conjecture about micro weights in positive characteristics. For each of these examples we determine the dimension and the Newton slopes of the ghost Abelian variety…

This brief article gives an alternative interpretation, based on a theorem of Berkovich, of the Eisenstein classes in the cohomology of Shimura varieties, used in forthcoming work of the author with K. W. Lan, R. Taylor, and J. Thorne.

We study the limiting behavior of extremal cohomology groups of $k$-points configuration spaces of complex projective spaces of complex dimension $m\geq 4.$ In the previous work, we prove that the extremal cohomology groups of degrees…

For n>2, we prove the mod 2 cohomology of the finite Chevalley group Spin_n(F_q) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).

Ghost condensates of dimension two are analysed in a class of nonlinear gauges in pure Yang-Mills theories. These condensates are related to the breaking of the SL(2,R) symmetry, present in these gauges.

We consider the conormal bundle of a Schubert variety $S_I$ in the cotangent bundle $T^* Gr$ of the Grassmannian $Gr$ of $k$-planes in $C^n$. This conormal bundle has a fundamental class ${\kappa_I}$ in the equivariant cohomology…

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected…

The rank 1 bosonic ghost vertex algebra, also known as the $\beta \gamma$ ghosts, symplectic bosons or Weyl vertex algebra, is a simple example of a conformal field theory which is neither rational, nor $C_2$-cofinite. We identify a module…

We give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by using the ghostness of a shriek map. Moreover, in a derived category, we discuss the triviality of the shriek map which induces…

We study $c<1$ matter coupled to gravity in the Coulomb gas formalism using the double cohomology of the string BRST and Felder BRST charges. We find that states outside the primary conformal grid are related to the states of non-zero ghost…

To each finite subset of $\mathbb{Z}^2$ (a diagram), one can associate a subvariety of a complex Grassmannian (a diagram variety), and a representation of a symmetric group (a Specht module). Liu has conjectured that the cohomology class of…

Let $\Gamma_{2n}^\omega(p)$ be the level-$p$ principal congruence subgroup of $\text{Sp}_{2n}(\mathbb{Z})$ for all prime $p$. Borel--Serre demonstrated that the cohomology of $\Gamma_{2n}^\omega(p)$ vanishes above degree $n^2$. We prove…

We prove vanishing results for the coherent cohomology of the good reduction modulo $p$ of the Siegel variety with coefficients in some automorphic bundles. We show that for an automorphic bundle with highest weight $\lambda$ near the walls…