Related papers: Poitou-Tate duality over extensions of global fiel…

In this paper, we establish a Poitou-Tate's global duality for totally positive Galois cohomology. We illustrate this result in the case of the twisted module "\`a la Tate" $\mathbb{Z}_{2}(i)$, $i$ integer.

We complete the picture of local and global arithmetic duality theorems for short complexes of finite Galois modules and tori over $p$-adic function fields. In view of the duality theorems, we deduce a $12$-term Poitou--Tate exact sequence…

The Poitou-Tate sequence relates Galois cohomology with restricted ramification of a finite Galois module $M$ over a global field to that of the dual module under the assumption that $\#M$ is a unit away from the allowed ramification set.…

Poitou-Tate duality for the Galois group of an extension of a global field with appropriately restricted ramification can be seen as taking place between the cohomology of a compact or discrete module and the compactly-supported cohomology…

We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on…

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…

We give a generalization of Poitou-Tate duality to schemes of finite type over rings of integers of global fields.

We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a systematic way. We describe field extensions…

If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove…

We prove several duality theorems for the Galois and etale cohomology of 1-motives defined over local and global fields and establish a 12-term Poitou-Tate type exact sequence. The results give a common generalisation and sharpening of…

We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact…

Let p be an odd prime. We consider the cyclotomic extension T := Z_(p)[zeta_{p^2}] of S := Z_(p), with galois group G := (Z/p^2)^*. Since this extension is wildly ramified, the SG-module T is not projective. We calculate its cohomology ring…

We compute the Galois cohomology of any $p$-adic valuation field extension of a pre-perfectoid field. Moreover, we obtain a generalization and also a new proof of the classical results of Tate and Hyodo on discrete valuation fields, without…

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then…

We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the subject, we discuss how to model the compactly supported side…

We establish duality results for the cohomology of the Weil group of a $p$-adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama…

Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When…

We investigate criteria for algebra extensions that are of Galois type with respect to the coaction of a Hopf algebra or, more generally, a one-sided quotient of a Hopf algebra, or with respect to an entwining. We study the module- and…

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.…

For fields F of characteristic not p containing a primitive $p$th root of unity, we determine the Galois module structure of the group of $p$th-power classes of K for all cyclic extensions K/F of degree p.