The derived de Rham complex has been introduced by Illusie in 1972 as a natural consequence of the definition of the cotangent complex for a scheme morphism. This theory seems to have been forgot until the recents works by Bhatt and Beilinson, who gave several applications, in particular in $p$-adic Hodge Theory. On the other hand, the derived de Rham cohomology has a crucial role in a conjecture by Flach-Morin about special values of zeta functions for arithmetic schemes. The aim of this thesis is to study and compute the Hodge completed derived de Rham complex in some cases.
La coomologia di de Rham derivata é stata introdotta da Luc Illusie nel 1972, in seguito ai suoi lavori sul complesso cotangente. Tale teoria sembra essere stata dimenticata fino ai lavori recenti di Bhatt e Beilinson, i quali ne hanno fornito diverse applicazioni, in particolare nella teoria $p$-adica di Hodge. D'altra parte, la coomologia di de Rham derivata interviene in maniera cruciale in una congettura di Flach-Morin sui valori speciali della funzione zeta di schemi aritmetici. In questa tesi ci proponiamo di studiare e calcolare la coomologia di de Rham derivata in certi casi.
ON DERIVED DE RHAM COHOMOLOGY / D.m.a. Marangoni ; supervisors: B. Morin (Université de Bordeaux), N. Mazzari (Università degli Studi di Padova) ; coordinator: V. Mastropietro. Università degli Studi di Milano, 2020 Jul 28. 32. ciclo, Anno Accademico 2019. [10.13130/marangoni-davide-maria-alfonso_phd2020-07-28].
ON DERIVED DE RHAM COHOMOLOGY
D.M.A. Marangoni
2020
Abstract
The derived de Rham complex has been introduced by Illusie in 1972 as a natural consequence of the definition of the cotangent complex for a scheme morphism. This theory seems to have been forgot until the recents works by Bhatt and Beilinson, who gave several applications, in particular in $p$-adic Hodge Theory. On the other hand, the derived de Rham cohomology has a crucial role in a conjecture by Flach-Morin about special values of zeta functions for arithmetic schemes. The aim of this thesis is to study and compute the Hodge completed derived de Rham complex in some cases.File | Dimensione | Formato | |
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phd_unimi_R11597.pdf
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Descrizione: Tesi di dottorato "On derived de Rham cohomology"
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