Related papers: Evaluation of Brauer elements over local fields

Let M be a smooth manifold, A a local algebra in sense of Andr\'e Weil, M^{A} the manifold of near points on M of kind A and X(M^{A}) the module of vector fields on M^{A}. We give a new definition of vector fields on M^{A} and we show that…

In 2017, Green and Schroll introduced a generalization of Brauer graph algebras which they call Brauer configuration algebras. In the present paper, we further generalize Brauer configuration algebras to fractional Brauer configuration…

The present paper illustrates the utility of Brauer relations, Galois covers of curves and the theory of regulator constants in the context of studying isogenies between Jacobians and their relevance to the parity conjecture. This framework…

We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.

We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…

Let D be a central division algebra over a field F. We study in this note the rigidity of the motivic decompositions of the Severi-Brauer varieties of D, with respect to the ring of coefficients and to the base field. We first show that if…

We suggest a twisted version of the categorical McKay correspondence and prove several results related to it.

We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…

We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…

Let $k$ be an algebraically closed field of a prime characteristic $p$. Let $G$ be a finite group. We investigate the Brauer indecomposability of Scott $kG$-modules in relation to the kernel of modules. We generalize a criterion for Brauer…

We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…

The classical Brauer-Siegel conjecture describes the asymptotic behaviour of the product of the class number and the regulator in families of number fields. All known cases of the conjecture rely on reducing the problem, via group theoretic…

The study of the moduli of covers of the projective line leads to the theory of Hurwitz varieties covering configuration varieties. Certain one-dimensional slices of these coverings are particularly interesting Belyi maps. We present…

We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras $B_2$ and $G_2$ over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of…

Theory for open curves over a local field. After introducing the reciprocity map, we determine the kernel and the cokernel of this map. In addition to this, the Pontrjagin dual of the reciprocity map is also investigated. This gives the one…

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

To locate all eigenvalues of a matrix more precisely, we exclude some sets which do not include any eigenvalue of the matrix from the well-known Brauer set to give two new Brauer-type eigenvalue inclusion sets. And it is also shown that the…

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

For a smooth projective variety X over an arbitrary field k, we discuss the surjectivity of the Albanese map from the Chow group of zero-cycles of degree zero on X to the group of rational points of the Albanese variety of X. Over…

We discuss convergence in the Fourier algebra A(G) of a locally compact group G and provide a new characterisation of the local spectral sets of G.