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The existence of equivariant pure free resolutions

David EisenbudGunnar FløystadJerzy Weyman — 2011

Annales de l’institut Fourier

Let A = K [ x 1 , , x m ] be a polynomial ring in m variables and let d = ( d 0 < < d m ) be a strictly increasing sequence of m + 1 integers. Boij and Söderberg conjectured the existence of graded A -modules M of finite length having pure free resolution of type d in the sense that for i = 0 , , m the i -th syzygy module of M has generators only in degree d i . This paper provides a construction, in characteristic zero, of modules with this property that are also G L ( m ) -equivariant. Moreover, the construction works over...

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