Böckle, Gebhard Cohomological theory of crystals over function fields and applications. (English) Zbl 1386.11076 Bars, Francesc (ed.) et al., Arithmetic geometry over global function fields. Selected notes based on the presentations at five advanced courses on arithmetic geometry at the Centre de Recerca Matemàtica, CRM, Barcelona, Spain, February 22 – March 5 and April 6–16, 2010. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0852-1/pbk; 978-3-0348-0853-8/ebook). Advanced Courses in Mathematics – CRM Barcelona, 1-118 (2014). Summary: This lecture series introduces in the first part a cohomological theory for varieties in positive characteristic with finitely generated rings of this characteristic as coefficients developed jointly with Richard Pink. In the second part various applications are given.For the entire collection see [Zbl 1305.11001]. Cited in 8 Documents MSC: 11G09 Drinfel’d modules; higher-dimensional motives, etc. 11F52 Modular forms associated to Drinfel’d modules 14F30 \(p\)-adic cohomology, crystalline cohomology Keywords:modular form; short exact sequence; trace formula; Galois representation; cohomological theory Software:NEWUOA; ABC4EFT; Resultants; REPSN; StableBBasisNBM5; PurityFiltration; Genius; LiE; COBYLA2; AIM@SHAPE; Newmat PDFBibTeX XMLCite \textit{G. Böckle}, in: Arithmetic geometry over global function fields. Selected notes based on the presentations at five advanced courses on arithmetic geometry at the Centre de Recerca Matemàtica, CRM, Barcelona, Spain, February 22 -- March 5 and April 6--16, 2010. Basel: Birkhäuser/Springer. 1--118 (2014; Zbl 1386.11076) Full Text: DOI References: [1] Anderson, G., t-motives, Duke Math. J. 53 (1986), 457-502. · Zbl 0679.14001 [2] Anderson, G., An elementary approach to L-functions mod p, J. 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