Related papers: On a generalized Brauer group in mixed characteris…

We consider a class of metabelian groups first studied by Baumslag and Stammbach and we show that these groups are consistent with the Bieri-Groves conjecture which relates cohomological finiteness conditions to the Bieri-Neumann-Strebel…

We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these…

Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after…

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the…

We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group $S_n$ on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural…

Assuming the K\"unneth type standard conjecture, we propose a way to describe objects of mixed motives explicitly. We study their formal properties, and we associate mixed motives to schemes smooth and separated over a field. This serves as…

We prove a general result on the depth of Du Bois complexes of a singular variety. We apply it to prove a conjecture of Mustata-Popa and to study the local cohomological defect, extending results of Ogus and Dao-Takagi over the complex…

We perform Hochschild homology calculations in the algebro-geometric setting of motives. The motivic Hochschild homology coefficient ring contains torsion classes which arise from the mod-$p$ motivic Steenrod algebra and from generating…

Suppose that $B$ is a Brauer $p$-block of a finite group $G$ with a unique modular character $\varphi$. We prove that $\varphi$ is liftable to an ordinary character of $G$ (which moreover is $p$-rational for odd $p$). This confirms the…

We extend Tate duality for Galois cohomology of abelian varieties to $1$-motives over a $p$-adic field, improving a result of Harari and Szamuely. To do this, we replace Galois cohomology with the condensed cohomology of the Weil group.…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…

We provide a formula (see Theorem 1.5) for the Matlis dual of the injective hull of $R/\mathfrak{p}$ where $\mathfrak p$ is a one dimensional prime ideal in a local complete Gorenstein domain $(R,\mathfrak{m})$. This is related to results…

We prove that the motivic cohomology of mixed characteristic schemes, introduced in our previous work, satisfies various expected properties of motivic cohomology, including a motivic refinement of Weibel's vanishing in algebraic…

In characteristic 0 there are essentially two approaches to the conjectural theory of mixed motives, one due to Nori and the other one due to, independently, Hanamura, Levine, and Voevodsky. Although these approaches are apriori quite…

We show that Grothendieck's standard conjectures are implied by either of two other motivic conjectures: (a) by that of the existence of the motivic t-structure, and (b) by (a weak form of) Suslin's Lawson homology conjecture.

A proof of a theorem of M. Hertweck presented during a seminar in January 2013 in Stuttgart is given. The proof is based on a preprint given to me by Hertweck. Let $R$ be a commutative ring, $G$ a finite group, $N$ a normal $p$-subgroup of…

We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with $h^{2, 0} = 1$, under a mild assumption on moduli. By refining this general result, we establish a new case of…

Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…

In [AGRS] a multiplicity one theorem is proven for general linear groups, orthogonal groups and unitary groups ($GL, O,$ and $U$) over $p$-adic local fields. That is to say that when we have a pair of such groups $G_n\subseteq G_{n+1}$, any…