Related papers: Characteristic 0 and p analogies, and some motivic…

We formulate a conjecture on the motivic McKay correspondence for the group scheme $ \alpha_{p}$ in characteristic $p>0$ and give a few evidences. The conjecture especially claims that there would be a close relation between quotient…

Following the idea of an invariant differential complex, we construct general-type cyclic modules that provide the common denominator of known cyclic theories. The cyclicity of these modules is governed by Hopf-algebraic structures. We…

Over the complex numbers, we compute the $C_2$-equivariant Bredon motivic cohomology ring with $\mathbb{Z}/2$ coefficients. By rigidity, this extends Suslin's calculation of the motivic cohomology ring of algebraically closed fields of…

Let $A$ be a ring and $R$ be a polynomial or a power series ring over $A$. When $A$ has dimension zero, we show that the Bass numbers and the associated primes of the local cohomology modules over $R$ are finite. Moreover, if $A$ has…

We prove that, over a perfect field, Bredon motivic cohomology can be computed by Suslin-Friedlander complexes of equivariant equidimensional cycles. Partly based on this result we completely identify Bredon motivic cohomology of a…

Let $k$ be a field of positive characteristic $p$, and $X$ be a separated of finite type $k$-scheme of dimension $d$. We construct a cycle map from the additive cycle complex to the residual complex of Serre-Grothendieck coherent duality…

Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use…

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

In the model of synthetic differential geometry consisting of sheaves (with respect to open covers) over the opposite category of the category of closed finitely generated C-infinity rings, any morphism from S, the zeroes of the "amazing…

Let $k$ be a field of characteristic zero and I an ideal defining an arrangement of linear subspaces in the affine space $A^n_k$. We compute the D-module theoretic characteristic cycle of the local cohomology modules $H^r_I(k[x_1,...,x_n])$…

We explain that a new theorem of Deligne on symmetric tensor categories implies, in a straightforward manner, that any finite dimensional triangular Hopf algebra over an algebraically closed field of characteristic zero has Chevalley…

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of the projective line with ramification to order e_i at general points P_i, in the case…

We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…

In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then…

A p-typical cover of a connected scheme on which p=0 is a finite etale cover whose monodromy group (i.e., the Galois group of its normal closure) is a p-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors;…

In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our main objective is to furnish a purely…

Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…