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Award ID contains: 1701659

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  1. ; (, Communications in Number Theory and Physics)
    Full Text Available 
  2. ; ; (, Duke mathematical journal)
    We exhibit families of smooth projective threefolds with both stably rational and non stably rational fibers. 
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    Accepted Manuscript Full Text Available
  3. ; (, Nagoya Mathematical Journal)
    Abstract We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups. 
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  4. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Given a smooth projective variety over a number field and an elementof its Brauer group, we consider the specialization of the Brauerclass at a place of good reduction for the variety and the class. Weare interested in the case of K3 surfaces.We show that a Brauer class on a very general polarized K3 surfaceover a number field becomes trivial after specialization at a set ofplaces of positive natural density. We deduce that there exist cubic fourfolds over number fields that are conjecturally irrational, with rational reduction at a positive proportion of places. We also deduce that there are twisted derivedequivalent K3 surfaces which become derived equivalent after reductionat a positive proportion of places. 
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  5. ; ; ; (, Selecta Mathematica)
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  6. ; (, Pure and Applied Mathematics Quarterly)
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  7. ; ; (, Commentarii Mathematici Helvetici)
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  8. ; (, Arithmetic geometry, number theory, and computation)
    Balakrishnan, J.S.; Elkies, N.; Hassett, B.; Poonen, B.; Sutherland, A.V.; Voight, J. (Ed.)
    In this article, we discuss whether a single congruent number t can have two (or more) distinct corresponding triangles with the same hypotenuse. We describe and carry out computational experimentation providing evidence that this does not occur. 
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    Accepted Manuscript Full Text Available
  9. ; (, European Journal of Mathematics)
    null (Ed.)
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  10. ; (, Lenseignement mathématique)
    null (Ed.)
    We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a non-closed field. (with an appendix by Jean-Louis Colliot-Thélène) 
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    Accepted Manuscript Full Text Available