Cohomological theory of crystals over function fields

DOI10.4171/074zbMath1186.14002OpenAlexW1486079046MaRDI QIDQ731482

Gebhard Böckle, Richard Pink

Publication date: 8 October 2009

Published in: EMS Tracts in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/074

zbMATH Keywords

cohomologytrace formulaL-functioncrystals\(\tau\)-sheavesA-motives

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Algebraic number theory: global fields (11R99) (p)-adic cohomology, crystalline cohomology (14F30)

Related Items

Tannakian properties of unit Frobenius-modules ⋮ Functorial test modules ⋮ Differential equations and Lie group representations ⋮ Resultantal varieties related to zeroes of \(L\)-functions of Carlitz modules ⋮ A class formula for admissible Anderson modules ⋮ The mod-\(p\) Riemann-Hilbert correspondence and the perfect site ⋮ Equivariant trace formula mod \(p\) ⋮ A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives ⋮ Congruences of Galois representations attached to effective A-motives over global function fields ⋮ The distribution of the zeros of the Goss zeta-function for \(A=\mathbb{F}_2[x,y/(y^2+y+x^3+x+1)\)] ⋮ Leading coefficient of the Goss Zeta value and p-ranks of Jacobians of Carlitz cyclotomic covers ⋮ \(A\)-expansions of Drinfeld modular forms ⋮ Cohomological Theory of Crystals over Function Fields and Applications ⋮ Special values of Goss \(L\)-series attached to Drinfeld modules of rank 2 ⋮ Trace formula for crystals with group actions ⋮ Arithmetic of positive characteristic -series values in Tate algebras ⋮ $V$-filtrations in positive characteristic and test modules ⋮ Special \(L\)-values of Drinfeld modules ⋮ Perfectoid Drinfeld modular forms ⋮ Uniformizable families of $t$-motives