The search session has expired. Please query the service again.
Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence.
The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a -cocycle corresponding to a higher metaplectic extension of GL for any global field . In the case that has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...
With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let be such a group. The stack of all representations of dimension is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack which is better behaved, and, in particular, admits a coarse algebraic space, which...
Currently displaying 1 –
20 of
27