Related papers: Kummer-Artin-Schreier-Witt Theory

Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is…

Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology,…

A family of exactly solvable models describing a spin-S Heisenberg chain doped with mobile spin-(S-1/2) carriers is constructed from gl(2|1)-invariant solutions of the Yang-Baxter equation. The models are generalizations of the…

We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We also study the compatibility of gauges and positive cones, and…

The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…

Let K be a finite extension of Q_p. The field of norms of a p-adic Lie extension K_infty/K is a local field of characteristic p which comes equipped with an action of Gal(K_infty/K). When can we lift this action to characteristic 0, along…

A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Ihara's lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate,…

We show that infinite families of non-relativistic spin-$3$ symmetries in $2+1$ dimensions, which include higher-spin extensions of the Bargmann, Newton-Hooke, non-relativistic Maxwell, and non-relativistic AdS-Lorentz algebras, can be…

We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue…

A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of $X=\mathcal{O}_{\mathbb{P}^{1}}(-1,-1)$ to the augmentation polynomial of Legendrian contact homology. We describe how to use this conjecture to compute genus zero,…

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…

Let k be a perfect field of characteristic p>0, let A_d be the coordinate ring of the coordinate axes in affine d-space over k, and let I_d be the ideal defining the origin. We evaluate the relative K-groups K_q(A_d,I_d) in terms of…

In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In…

In this series of three papers, we introduce and study cyclotomic pairs and smooth profinite groups. They are a geometric axiomatisation of Kummer theory for fields, with coefficients $p$-primary roots of unity, for a prime $p$. These…

The aim of this thesis is to present the notion of spaces whose curvature is bounded above, and to give some of its application in the context of Combinatorial Algebra. The thesis is made of two parts, one of theoretic purpose, and the…

We study a moduli space AS_g for Artin-Schreier curves of genus g over an algebraically closed field k of characteristic p. We study the stratification of AS_g by p-rank into strata AS_{g,s} of Artin-Schreier curves of genus g with p-rank…

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, we give some concrete examples and properties of strongly…

We use techniques of relative algebraic K-theory to develop a common refinement of the existing theories of metrized and hermitian Galois structures in arithmetic. As a first application of this very general approach, we then use it to…

Under hypotheses required for the Taylor-Wiles method, we prove for forms of $U(3)$ which are compact at infinity that the lattice structure on upper alcove algebraic vectors or on principal series types given by the $\lambda$-isotypic part…

Let $K$ be an arbitrary infinite field. The cohomology group $H^2(SL(2,K), H_2\,SL(2,K))$ contains the class of the universal central extension. When studying representations of fundamental groups of surfaces in $SL(2,K)$ it is useful to…