Explicit classification of formal groups over complete discrete valuation fields with imperfect residue field

2006 ◽  
pp. 1-29 ◽  
Author(s):  
M. V. Bondarko
Keyword(s):  
Residue Field ◽  
Formal Groups

scholarly journals On classification of typical representations for GL3(F)

2019 ◽  
Vol 31 (4) ◽  
pp. 917-941
Author(s):  
Santosh Nadimpalli
Keyword(s):  
Local Field ◽  
Residue Field ◽  
Principal Series

Abstract Let F be any non-Archimedean local field with residue field of cardinality {q_{F}} . In this article, we obtain a classification of typical representations for the Bernstein components associated to the inertial classes of the form {[\operatorname{GL}_{n}(F)\times F^{\times},\sigma\otimes\chi]} with {q_{F}>2} , and for the principal series components with {q_{F}>3} . With this we complete the classification of typical representations for {\operatorname{GL}_{3}(F)} , for {q_{F}>2} .

"The Empirical Classification of Formal Groups": Reply to Gold

1964 ◽  
Vol 29 (5) ◽  
pp. 739 ◽  
Author(s):  
Hanan C. Selvin ◽  
Warren O. Hagstrom
Keyword(s):  
Formal Groups

scholarly journals Valued fields with finitely many defect extensions of prime degree

2021 ◽  
pp. 2250049
Author(s):  
Franz-Viktor Kuhlmann
Keyword(s):  
Open Problem ◽  
Positive Characteristic ◽  
Residue Field ◽  
Prime Degree ◽  
Valued Fields ◽  
Mixed Characteristic ◽  
Valued Field ◽  
Field Of Positive Characteristic

We prove that a valued field of positive characteristic [Formula: see text] that has only finitely many distinct Artin–Schreier extensions (which is a property of infinite NTP2 fields) is dense in its perfect hull. As a consequence, it is a deeply ramified field and has [Formula: see text]-divisible value group and perfect residue field. Further, we prove a partial analogue for valued fields of mixed characteristic and observe an open problem about 1-units in this setting. Finally, we fill a gap that occurred in a proof in an earlier paper in which we first introduced a classification of Artin–Schreier defect extensions.

The Empirical Classification of Formal Groups

1963 ◽  
Vol 28 (3) ◽  
pp. 399 ◽  
Author(s):  
Hanan C. Selvin ◽  
Warren O. Hagstrom
Keyword(s):  
Formal Groups
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