scholarly journals Integral p-adic Hodge theory of formal schemes in low ramification

2021 ◽  
Vol 15 (4) ◽  
pp. 1043-1076
Author(s):  
Yu Min
Keyword(s):  
Hodge Theory ◽  
Formal Schemes

Shtukas with one leg

2020 ◽  
pp. 98-107
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Hodge Theory ◽  
Formal Schemes ◽  
Geometric Point ◽  
Divisible Groups ◽  
Special Case ◽  
General Connection

This chapter analyzes shtukas with one leg over a geometric point in detail, and discusses the relation to (integral) p-adic Hodge theory. It focuses on the connection between shtukas with one leg and p-divisible groups, and recovers a result of Fargues which states that p-divisible groups are equivalent to one-legged shtukas of a certain kind. In fact this is a special case of a much more general connection between shtukas with one leg and proper smooth (formal) schemes. Throughout, the goal is to fix an algebraically closed nonarchimedean field. The chapter then provides an overview of shtukas with one leg and p-divisible groups.

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

Harmonic Maps and Hodge Theory

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

scholarly journals $p$-adic Hodge theory

1988 ◽  
Vol 1 (1) ◽  
pp. 255-255
Author(s):  
Gerd Faltings
Keyword(s):  
Hodge Theory
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