scholarly journals -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES – CORRIGENDUM

2016 ◽  
Vol 4 ◽  
Author(s):  
PETER SCHOLZE
Keyword(s):  
Hodge Theory ◽  
Analytic Varieties

The author would like to make some changes to the previously published article [1] by correcting two definitions.

scholarly journals -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES

2013 ◽  
Vol 1 ◽  
Author(s):  
PETER SCHOLZE
Keyword(s):  
Hodge Theory ◽  
Analytic Varieties ◽  
De Rham ◽  
Perfectoid Spaces

AbstractWe give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-étale site, which makes all constructions completely functorial.

Teichmüller dynamics and unique ergodicity via currents and Hodge theory

2020 ◽  
Vol 2020 (768) ◽  
pp. 39-54
Author(s):  
Curtis T. McMullen
Keyword(s):  
Hodge Theory ◽  
Unique Ergodicity ◽  
Polygonal Billiards ◽  
Teichmuller Dynamics

AbstractWe present a cohomological proof that recurrence of suitable Teichmüller geodesics implies unique ergodicity of their terminal foliations. This approach also yields concrete estimates for periodic foliations and new results for polygonal billiards.

scholarly journals Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

2015 ◽  
Vol 30 (20) ◽  
pp. 1550115 ◽  
Author(s):  
D. Shukla ◽  
T. Bhanja ◽  
R. P. Malik
Keyword(s):  
Present Method ◽  
Hodge Theory ◽  
Rigid Rotor ◽  
Normal Ordering ◽  
Creation And Annihilation Operators ◽  
Basic Concepts ◽  
Definition Of ◽  
Continuous Symmetries ◽  
Internal Symmetries ◽  
Theory Lead

We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one [Formula: see text]-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.

scholarly journals Almost direct summands

2014 ◽  
Vol 214 ◽  
pp. 195-204 ◽  
Author(s):  
Bhargav Bhatt
Keyword(s):  
Direct Summand ◽  
Hodge Theory ◽  
Fundamental Theorems ◽  
Ramification Locus

AbstractWe prove new cases of the direct summand conjecture using fundamental theorems inp-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristicp.

scholarly journals Hodge Theory of the Middle Convolution

2013 ◽  
Vol 49 (4) ◽  
pp. 761-800 ◽  
Author(s):  
Michael Dettweiler ◽  
Claude Sabbah
Keyword(s):  
Hodge Theory ◽  
Middle Convolution

scholarly journals A motivic version of the theorem of Fontaine and Wintenberger

2018 ◽  
Vol 155 (1) ◽  
pp. 38-88 ◽  
Author(s):  
Alberto Vezzani
Keyword(s):  
Galois Groups ◽  
Rational Homotopy ◽  
Mixed Characteristic ◽  
Homotopy Invariant ◽  
Analytic Varieties

We establish a tilting equivalence for rational, homotopy-invariant cohomology theories defined over non-archimedean analytic varieties. More precisely, we prove an equivalence between the categories of motives of rigid analytic varieties over a perfectoid field $K$ of mixed characteristic and over the associated (tilted) perfectoid field $K^{\flat }$ of equal characteristic. This can be considered as a motivic generalization of a theorem of Fontaine and Wintenberger, claiming that the Galois groups of $K$ and $K^{\flat }$ are isomorphic.

Harmonic Maps and Hodge Theory

2017 ◽  
pp. 383-402
Author(s):  
James Carlson ◽  
Stefan Muller-Stach ◽  
Chris Peters
Keyword(s):  
Harmonic Maps ◽  
Hodge Theory
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