Related papers: Ramification theory for reciprocity sheaves, III, …

For a Henselian discrete valued field $K$ of characteristic $p>0$, Kato defined a ramification filtration $\{{\rm fil}_nH^q(K,\mathbb Q_p/\mathbb Z_p(q-1))\}_{n \ge 0}$ on $H^q(K,\mathbb Q_p/\mathbb Z_p(q-1))$. One can also define a…

We introduce a theory of motivic cohomology for quasi-compact quasi-separated schemes, which generalises the construction of Elmanto--Morrow in the case of schemes over a field. Our construction is non-$\mathbb{A}^1$-invariant in general,…

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…

Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive…

As a sequel of Part I, we consider a filtration of Hodge cohomology groups indexed by divisors "at infinity", and prove that they are represented in the category of motives with modulus. In particular, we obtain a realisation functor of the…

We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gauge theories on $\mathbb{R}^4$ and with two-dimensional…

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 define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate…

We introduce an etale fundamental group with modulus and construct a reciprocity homomorphism from the Kato-Saito idele class group with modulus to this fundamental group. This is the K-theoretic analogue of the reciprocity for the…

For a constructible \'etale sheaf on a smooth variety of positive characteristic ramified along an effective divisor, the largest slope in Abbes and Saito's ramification theory of the sheaf gives a divisor with rational coefficients called…

In his article "Unitary Representations and Complex Analysis", David Vogan gives a characterization of the continuous invariant Hermitian forms defined on the compactly supported sheaf cohomology groups of certain homogeneous analytic…

In this paper, we continue the program initiated by Kahn-Saito-Yamazaki by constructing and studying an unstable motivic homotopy category with modulus, extending the Morel-Voevodsky construction from smooth schemes over a field $k$ to…

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification…

We consider a tamely ramified abelian extension of local fields of degree n, without assuming the presence of the nth roots of unity in the base field. We give an explicit formula which computes the local reciprocity map in this situation.

We investigate the positivity and extension of invertible sheaves on group homogeneous spaces over coherent bases. Bypassing the failure of standard limit arguments and the classical Weil--Cartier correspondence, we develop a valuative…

Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…

We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the…

Formal orbifolds are defined in higher dimension. Their \'etale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

We study the cohomology of reflexive rank 2 sheaves on smooth projective threefolds. Applications are given to the moduli space of reflexive sheaves.