Related papers: Galois Codescent For Motivic Tame Kernels

We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the element corresponding to the stable Hopf map is inverted in…

Let D be a central simple algebra of prime degree over a field and let E be an SL_1(D)-torsor. We determine the complete motivic decomposition of certain compactifications of E. We also compute the Chow ring of E.

Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable extension of local fields, $\left[ L:K\right] =p^{n},\;n\geq2.$ It is known that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act on the…

Suppose $\mathcal K$ is $N$-dimensional local field of characteristic $p$, $\mathcal G =\mathop{Gal}(\mathcal K_{sep}/\mathcal K)$, $\mathcal G_{<p}$ is the maximal quotient of $\mathcal G$ of period $p$ and nilpotent class $<p$ and…

We generalize the theory of the second invariant cohomology group $H^2_{\rm inv}(G)$ for finite groups $G$, developed in [Da2,Da3,GK], to the case of affine algebraic groups $G$, using the methods of [EG1,EG2,G]. In particular, we show that…

Given a global field K and a rational function phi defined over K, one may take pre-images of 0 under successive iterates of phi, and thus obtain an infinite rooted tree T by assigning edges according to the action of phi. The absolute…

A (projective, geometrically irreducible, non-singular) curve $\mathcal{X}$ defined over a finite field $\mathbb{F}_{q^2}$ is maximal if the number $N_{q^2}$ of its $\mathbb{F}_{q^2}$-rational points attains the Hasse-Weil upper bound, that…

This is a continuation of the authors' study of finite-dimensional pointed Hopf algebras H which act inner faithfully on commutative domains. As mentioned in Part I of this work, the study boils down to the case where H acts inner…

Let $K$ be a number field and $k\geq 2$ be an integer. Let $(n_1,n_2, \dots, n_k)$ be a vector with entries $n_i\in \mathbb{Z}_{\geq 2}$. Given a number field extension $L/K$, we denote by $\widetilde{L}$ the Galois closure of $L$ over $K$.…

Let $X\to Y^0$ be an abelian prime-to-$p$ Galois covering of smooth schemes over a perfect field $k$ of characteristic $p>0$. Let $Y$ be a smooth compactification of $Y^0$ such that $Y-Y^0$ is a normal crossings divisor on $Y$. We describe…

A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of…

We consider a complex of tori of length 2 defined over a number field k. We establish here some local and global duality theorems for the (\'etale or Galois) hypercohomology of such a complex. We prove the existence of a Poitou-Tate exact…

Let k be a field of characteristic 2 and let L/k be a finite Galois extension with Galois group G. We show the equivalence of the following two properties: (*) The group G is generated by elements of order 2 and by elements of odd order.…

For a prime number $\ell$ and an extension of number fields $K/F$, we prove new lower bounds on the $\ell$-rank of the ideal class group of $K$ based on prime ramification in $K/F$. Unlike related results from the literature, our bound is…

In this paper we obtain new quantitative forms of Hilbert's Irreducibility Theorem. In particular, we show that if $f(X, T_1, \ldots, T_s)$ is an irreducible polynomial with integer coefficients, having Galois group $G$ over the function…

Let $X$ be a compact K\"{a}hler manifold, and let $L$ be a line bundle on $X.$ Define $I_k(L)$ to be the kernel of the multiplication map $ Sym^k H^0 (L) \to H^0 (L^k).$ For all $h \leq k,$ we define a map $\rho : I_k(L) \to Hom (H^{p,q}…

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck-Witt ring of the base field. Previous work of the first author and recent work of…

Given a finite and connected two-dimensional $CW$-complex $K$ with fundamental group $\Pi$ and second integer cohomology group $H^2(K;\mathbb{Z})$ finite of odd order, we prove that: (1) for each local integer coefficient system…

Balmer and Dell'Ambrogio introduced the pseudo-functor $P$ from the bicategory of $k$-linear Mackey $2$-motives to the bicategory of $k$-linear cohomological Mackey $2$-motives over a commutative ring $k$. They showed that $P$ maps the…