Properties (56)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical Concept
|
| gptkbp:are |
A subject of interest in the context of derived categories
A concept that has reshaped certain areas of mathematics A part of the landscape of modern algebraic geometry A bridge between algebra and geometry A class of spaces in algebraic geometry A concept that emerged in the 21st century A generalization of the notion of a perfect field A key concept in modern number theory A subject of active research in mathematics A subject of graduate-level study in mathematics A topic in the study of algebraic topology A topic of discussion in mathematical conferences Integral over a perfectoid ring A concept that has led to new discoveries in number theory Used in the context of crystalline cohomology Used in the study of local fields A significant advancement in the field of arithmetic geometry A framework for understanding the interplay between algebra and geometry A significant area of research in contemporary mathematics A significant topic in the field of arithmetic algebraic geometry A concept that has implications for the theory of motives. A framework for understanding the behavior of p-adic forms A_key_concept_in_the_theory_of_perfectoid_rings A_tool_for_understanding_the_Langlands_program Related_to_the_theory_of_perfectoid_fields A_focus_of_interest_for_mathematicians_studying_Galois_theory |
| gptkbp:canLeadTo |
The study of étale cohomology
The_study_of_algebraic_K-theory |
| gptkbp:characterizedBy |
gptkb:Perfectoid_Rings
|
| gptkbp:developedBy |
gptkb:Peter_Scholze
|
| gptkbp:has |
Applications in the study of motives
Connections to the theory of schemes Implications for the study of modular forms Applications in the study of rational points on varieties Influenced the development of new mathematical tools Connections_to_the_theory_of_algebraic_cycles Implications_for_the_study_of_algebraic_groups |
| gptkbp:hasClient |
Tate's_Theory
|
| gptkbp:hasRelatedPatent |
Number Theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Perfectoid Spaces
|
| gptkbp:includes |
gptkb:Topological_Spaces
|
| gptkbp:interactsWith |
Formal Schemes
|
| gptkbp:isCounteredBy |
Their cohomological properties
|
| gptkbp:isUsedFor |
gptkb:Spectral_Sequences
Homotopy Theory The theory of motives Investigate the properties of algebraic varieties Study the reduction of schemes Study the structure of algebraic varieties The study of local systems Mathematical_Journals |
| gptkbp:provides |
New insights into the study of Galois representations
|
| gptkbp:relatedTo |
p-adic Geometry
|
| gptkbp:standardFeatures |
Classical_Spaces
|
| gptkbp:usedIn |
Arithmetic Geometry
|