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In this paper, we describe a new infinite family of q 2 −1 2-tight sets in the hyperbolic quadrics Q + (5, q), for q ≡ 5 or 9 mod 12. Under the Klein correspondence, these correspond to Cameron–Liebler line classes of PG(3, q) having parameter q 2 −1 2. This is the second known infinite family of nontrivial Cameron–Liebler line classes, the first family… (More)
A Cameron-Liebler line class in PG(3, q) is a set L of x(q 2 + q + 1) lines of PG(3, q) with the property that any spread of PG(3, q) shares exactly x lines with L. In the talk, which reports on joint work with Jeroen Demeyer, Klaus Metsch and Morgan Rodgers, we will overview some non-existence results of Cameron-Liebler line classes for relatively small… (More)
Let K be a field with a valuation satisfying the following conditions: both K and the residue field k have characteristic zero; the value group is not 2-divisible; there exists a maximal subfield F in the valuation ring such that Gal(¯ F /F) and Gal(¯ k/k) have the same 2-cohomological dimension and this dimension is finite. Then Hilbert's Tenth Problem has… (More)
As developers of SageMath, we show how open software facilitates corrections. " Commercial computer algebra systems are black boxes, and their algorithms are opaque to the users, " complained a trio of mathematicians whose " misfortunes " are detailed in a recent Notices article . " We reported the bug on October 7, 2013…By June 2014, nothing had changed… (More)
Let R be a recursive noetherian integral domain of characteristic zero with fraction field K. Assume that K is finitely generated (as a field) over Q. Equivalently, assume that K is the function field of a variety over a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z].
Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T ]. We show that the set of polynomials with integer coefficients is diophantine over R[T ]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T ] k is diophantine over R[T ].