Grothendieck at Pisa: crystals and Barsotti-Tate groups

@inproceedings{Illusie2015GrothendieckAP,
  title={Grothendieck at Pisa: crystals and Barsotti-Tate groups},
  author={Luc Illusie},
  year={2015}
}
Grothendieck visited Pisa twice, in 1966, and in 1969. It is on these occasions that he conceived his theory of crystalline cohomology and wrote foundations for the theory of deformations of p-divisible groups, which he called Barsotti-Tate groups. He did this in two letters, one to Tate, dated May 1966, and one to me, dated Dec. 2–4, 1969. Moreover, discussions with Barsotti that he had during his first visit led him to results and conjectures on specialization of Newton polygons, which he… 
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