Project description

The aim of this proposal is to apply the methods and insights gained in the setting of motives to a concrete object of general interest: the sheaf of differential forms, with applications in birational geometry in mind. Of particular interest is the case of positive characteristic, where from many points of view we do not yet have a satisfactory theory. 

Related publications

Published Articles

Shane Kelly, Voevodsky motives and ldh descent. Astérisque 391 (2017).

Annette Huber, Differential forms in algebraic geometry -- a new perspective in the singular case. Portugaliae Mathematica 73 (2016), no. 4, 337--367.

Ofer Gabber, Shane Kelly, Points in algebraic geometry. J. Pure Appl. Algebra 219 (2015), no. 10, 4667–4680.

Annette Huber, Shane Kelly, Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces .Algebra Number Theory 12 (2018), no. 3, 649–692.

Annette Huber, Stefan Kebekus, Shane Kelly, Differential forms in positive characteristic avoiding resolution of singularities. Bull. Soc. Math. France 145 (2017), no. 2, 305–343.

Shane Kelly, Un isomorphisme de Suslin. Bull. Soc. Math. France 146 (2018), no. 4, 633–647.

Shane Kelly, Shuji Saito, Weight homology of motives. Int. Math. Res. Not. IMRN 2017, no. 13, 3938–3984.

Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field. ``Bousfield classes and Ohkawa's theorem'', 221–243, Springer Proc. Math. Stat., 309, Springer, Singapore, [2020], ©2020.

Jens Niklas Eberhardt, Shane Kelly, Mixed Motives and Geometric Representation Theory in Equal Characteristic. Selecta Math. (N.S.) 25 (2019), no. 2, Paper No. 30, 54 pp.

Preprints