in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it p...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...

The goal of this paper is to construct trace maps for the six functor formalism motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also an $\infty$-enhancement such a formalism. In course $\infty$-enhancement, we need reinterpret in more functorial manner. This done by using Suslin-Voevodsky's relative cycle groups.

We prove an analogue for $p$-adic coefficients of the Deligne--Laumon theorem on local acyclicity curves. That is, overconvergent $F$-isocrystal $E$ a relative curve $f:U\rightarrow S$ admitting good compactification, we show that cohomology sheaves $\mathbf{R}f_!E$ are isocrystals if and only has constant Swan conductor at infinity.

the aim of this paper is to study the $(alpha‎, ‎gamma)$-prolongation of central extensions‎. ‎we obtain the obstruction theory for $(alpha‎, ‎gamma)$-prolongations and classify $(alpha‎, ‎gamma)$-prolongations thanks to low-dimensional cohomology groups of groups‎.

the aim of this paper is to study co-prolongations of central extensions. we construct the obstruction theory forco-prolongations and classify the equivalence classes of these by kernels of homomorphisms between 2-dimensional cohomology groups of groups.

We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation conditions on cohomology, we show that relative support varieties contain homological information on the modules involved. As an application, we provide a new c...

For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D?X whose support is simple normal crossing divisor, we construct cycle class mapcycX|D:CH0(X|D)?HNisd(X,KdM(OX,ID)) from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.