Smooth flat maps over commutative DG-rings

Frobenius closure and prime characteristic singularities

10.32469/10355/78133 ◽

2020 ◽

Author(s):

◽

Kyle Logan Maddox

Keyword(s):

Local Ring ◽

Local Cohomology ◽

Sufficient Condition ◽

Zariski Topology ◽

Prime Characteristic ◽

Joint Work ◽

University Of Missouri ◽

Mild Conditions ◽

Flat Maps ◽

The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This dissertation outlines several results about prime characteristic singularities for which the nilpotent part under the induced Frobenius action on local cohomology is either finite colength or the entire module, collectively referred to here as nilpotent singularities. First, we establish a sufficient condition for the finiteness of the Frobenius test exponent for a local ring and apply it to conclude that nilpotent singularities have finite Frobenius test exponent. In joint work with Jennifer Kenkel, Thomas Polstra, and Austyn Simpson, we show that under mild conditions nilpotent singularities descend and ascend along faithfully flat maps. Consequently, we then prove that the loci of primes which are weakly F-nilpotent and F-nilpotent are open in the Zariski topology for rings which are either F-finite or essentially of fiiite type over an excellent local ring.

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Coordinate systems for conformal cerebellar flat maps

NeuroImage ◽

10.1016/s1053-8119(00)91398-3 ◽

2000 ◽

Vol 11 (5) ◽

pp. S467 ◽

Cited By ~ 23

Author(s):

Monica K. Hurdal ◽

Ken Stephenson ◽

Phil Bowers ◽

De Witt Sumners ◽

David A. Rottenberg

Keyword(s):

Coordinate Systems ◽

Flat Maps

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Human cingulate cortex: Surface features, flat maps, and cytoarchitecture

The Journal of Comparative Neurology ◽

10.1002/cne.903590310 ◽

1995 ◽

Vol 359 (3) ◽

pp. 490-506 ◽

Cited By ~ 459

Author(s):

Brent A. Vogt ◽

Esther A. Nimchinsky ◽

Leslie J. Vogt ◽

Patrick R. Hof

Keyword(s):

Cingulate Cortex ◽

Surface Features ◽

Flat Maps

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Palmyra V. M. Monteiro: Latin American Flat Maps 1926–1964, Vol. 1: Mexico, Central America, West Indies (Austin, University of Texas Press, 1968, 95s.). Pp. xvi + 395. (Guides and Bibliographies Series: 2, Institute of Latin American Studies.)

Journal of Latin American Studies ◽

10.1017/s0022216x00004582 ◽

1969 ◽

Vol 1 (2) ◽

pp. 208-209

Author(s):

David J. Fox

Keyword(s):

Central America ◽

Latin American ◽

West Indies ◽

American Studies ◽

Latin American Studies ◽

University Of Texas ◽

Flat Maps

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Optimization method for creating semi-isometric flat maps of the cerebral cortex

10.1117/12.387731 ◽

2000 ◽

Cited By ~ 19

Author(s):

Bijan Timsari ◽

Richard M. Leahy

Keyword(s):

Cerebral Cortex ◽

Optimization Method ◽

Flat Maps

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The Motivic Group H−1,−1BM

The Norm Residue Theorem in Motivic Cohomology ◽

10.23943/princeton/9780691191041.003.0007 ◽

2019 ◽

pp. 95-102

Author(s):

Christian Haesemeyer ◽

Charles A. Weibel

Keyword(s):

Homology Groups ◽

Group Of Units ◽

Proper Maps ◽

Flat Maps

This chapter develops some more of the properties of the Borel–Moore homology groups 𝐻𝐵𝑀 −1,−1(𝑋). It shows that it is contravariant in 𝑋 for finite flat maps, and has a functorial pushforward for proper maps. If 𝑋 is smooth and proper (in characteristic 0), 𝐻𝐵𝑀 −1,−1(𝑋) agrees with 𝐻2𝒅+1,𝒅+1(𝑋, ℤ), and has a nice presentation, which this chapter explores in more depth. The main result in this chapter is the proposition that: if 𝑋 is a norm variety for ª and 𝑘 is 𝓁-special then the image of 𝐻𝐵𝑀 −1,−1(𝑋) → 𝑘× is the group of units 𝑏 such that ª ∪ 𝑏 vanishes in 𝐾𝑀 𝑛+1(𝑘)/𝓁. Again, this chapter also explores the historic trajectory of its equations.

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