By Luis Dieulefait,Gerd Faltings,D. R. Heath-Brown,Yu. V. Manin,B. Z. Moroz,Jean-Pierre Wintenberger

The 'Arithmetic and Geometry' trimester, held on the Hausdorff study Institute for arithmetic in Bonn, focussed on contemporary paintings on Serre's conjecture and on rational issues on algebraic types. The ensuing lawsuits quantity offers a contemporary evaluate of the topic for graduate scholars in mathematics geometry and Diophantine geometry. it's also crucial interpreting for any researcher wishing to maintain abreast of the newest advancements within the box. Highlights comprise Tim Browning's survey on purposes of the circle solution to rational issues on algebraic forms and in keeping with Salberger's bankruptcy on rational issues on cubic hypersurfaces.

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