Struct PerfectoidField 

pub struct PerfectoidField {
    pub name: String,
    pub residue_char: u64,
    pub is_alg_closed: bool,
    pub tilt_name: String,
}

A perfectoid field K with its residue characteristic p.

Fields

name: String

Description of the field (e.g., “C_p”, “Q_p^{\infty}”).

residue_char: u64

Residue characteristic p.

is_alg_closed: bool

Whether the field is algebraically closed (e.g., C_p).

tilt_name: String

Tilt field K^♭ (described by name).

Implementations

impl PerfectoidField

pub fn new( name: impl Into<String>, residue_char: u64, tilt_name: impl Into<String>, ) -> Self

Create a perfectoid field.

pub fn c_p(p: u64) -> Self

The completed algebraic closure C_p of Q_p.

pub fn q_p_cyclotomic(p: u64) -> Self

The infinite cyclotomic extension Q_p(ζ_{p^∞}).

pub fn residue_characteristic(&self) -> u64

Residue characteristic of this perfectoid field.

pub fn tilt_characteristic(&self) -> u64

The tilt K^♭ has characteristic p.

pub fn hodge_tate_description(&self, dim: usize) -> String

Description of the Hodge-Tate decomposition for a de Rham representation.

Trait Implementations

impl Clone for PerfectoidField

fn clone(&self) -> PerfectoidField

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for PerfectoidField

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for PerfectoidField

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.