相关论文: The fundamental group of period domains over finit…

The goal of this paper is to give an explicit formula for the l-adic cohomology of period domains over finite fields for arbitrary reductive groups. The result is a generalisation of the computation in math.AG/9907098 which treats the case…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

We present new classes of permutation polynomials over finite fields.

We make a list of finite simple groups whose group rings over a given field are serial.

After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…

Let K be an arbitrary field. We will determine explicitly all the nontrivial finite groups of essential dimension one over K.

We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any…

We define Langlands parameters for connected reductive groups over finite fields and formulate the Langlands correspondence for finite fields using these parameters.

We provide explicit identity bases for finite cyclic semigroups.

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

We show by means of various examples that many of the current definitions of the notion of fundamental domain of a Fuchsian group lack an extra condition ensuring that the domain differs from a measurable fundamental set at most by a null…

We exhibit an algorithm to compute a Dirichlet domain for a cofinite Fuchsian group Gamma. As a consequence, we compute the invariants of Gamma, including an explicit finite presentation for Gamma.

We classify all finite groups of essential dimension 2 over an algebraically closed field of characteristic 0.

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a finite field.

We determine the finite groups whose real irreducible representations have different degrees.

We survey recent progress in computing with finitely generated linear groups over infinite fields, describing the mathematical background of a methodology applied to design practical algorithms for these groups. Implementations of the…