Related papers: Characterizing maximal varieties via Bredon cohomo…

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type G2, focusing on the case of number fields and p-adic fields. In the same context we characterize the rational conjugacy classes of A2…

The Eisenbud--Goto conjecture states that $\operatorname{reg} X\le\operatorname{deg} X -\operatorname{codim} X+1$ for a nondegenerate irreducible projective variety $X$ over an algebraically closed field. While this conjecture is known to…

We study the birational geometry of varieties of maximal Albanese dimension. In particular we discuss criteria for a generically finite morphism of varieties of maximal Albanese dimension to be birational; we give a new characterization of…

We study a natural Hodge theoretic generalization of rational (or $\mathbb{Q}$-)homology manifolds through an invariant ${\rm HRH(Z)}$ where $Z$ is a complex algebraic variety. The defining property of this notion encodes the difference…

We study the maximal multiplicity locus of a variety $X$ over a field of characteristic $p>0$ that is provided with a finite surjective radical morphism $\delta:X\rightarrow V$, where $V$ is regular, for example, when…

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…

The Borel-Weil-Bott theorem describes the cohomology of line bundles over flag varieties. Here, one generalizes this theorem to a wider class of projective varieties : the wonderful varieties of minimal rank.

We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain…

We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each component of H^i_B(R) is finite dimensional…

A field $K$ is quasi-classical $d$-local if there exist fields $K=k_d,\dots,k_0$ with $k_{i+1}$ Henselian admissible discretely valued with residue field $k_i$, and $k_0$ quasi-finite. We prove a duality theorem for the Galois cohomology of…

Let X be a noetherian scheme defined over an algebraically closed field of positive characteristic p, and G be a finite group, of order divisible by p, acting on X. We introduce a refinement of the equivariant K-theory of X to take into…

We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The examples are lattices in different higher rank simple Lie…

Let F be a field, let G be its absolute Galois group, and let R(G, k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k_*(F) to the graded ring gr…

We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's…

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector…

We calculate the cobordism ring $\Omega^{C_2}_*$ of stably almost complex manifolds with involution, and investigate the $C_2$-spectrum $\Omega_{C_2}$ which represents it. We introduce the notion of a geometrically oriented $C_2$-spectrum,…

This thesis consists of two main parts. In the second part, we recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local…

In this paper, we compute the $RO(C_{pq})$-graded cohomology of $C_{pq}$-orbits. We deduce that in all the cases the Bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations. Further,…

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

This article investigates equivariant parametrized cellular cohomology, a cohomology theory introduced by Costenoble-Waner for spaces with an action by a compact Lie group $G$. The theory extends the $RO(G)$-graded cohomology of a $G$-space…