ÉTALE MORPHISMS OF SCHEMES Contents 1. Introduction 1 2 ...
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Description

  • exposé - matière potentielle : for general schemes
  • exposé
ETALE MORPHISMS OF SCHEMES Contents 1. Introduction 1 2. Conventions 2 3. Unramified morphisms 2 4. Three other characterizations of unramified morphisms 4 5. The functorial characterization of unramified morphisms 5 6. Topological properties of unramified morphisms 6 7. Universally injective, unramified morphisms 7 8. Examples of unramified morphisms 8 9. Flat morphisms 9 10. Topological properties of flat morphisms 11 11. Etale morphisms 11 12. The structure theorem 13 13.
  • unramified morphisms
  • etale morphisms of schemes contents
  • unramified homomorphism of local rings
  • differentials
  • etale morphisms of schemes
  • ramification locus
  • projective modules
  • ring map
  • module

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Nombre de lectures 31
Langue English

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Lecture 7
M.J. Flynn
EE 486 lecture 7: Integer Multiplication
M. J. Flynn
slides prepared by Albert Liddicoat and Hossam Fahmy
Computer Architectur e & Arithmetic Group1
Stanford University
Multiplication Add-and-Shift Algorithm
MultiplicandX61 1 0 MultiplierY0 1x5x 1 1 1 0 Partial ProductsPP0 0 0 1 1 0 ResultS301 1 1 1 0
Y X Shift 0
ALU ShiftP
Computer Architectur e & Arithmetic Group2
Stanford University
Parallel Multiplication Generation of PPs Using ROMs 1Simultaneous generation of partial products 4b x 4b Multiply Using 2Parallel reduction of partial products 256x8-bit ROM 8b x 8b Multiply Using 3Carry Propagate Addition (CPA) 256x8-bit ROMs X R Parallel generation of partial productsY X X X XX X X X 7 6 5 43 2 1 0 Y Y Y YY Y Y Y 7 6 5 43 2 1 0 x Using AND gate as 1x1-bit multiplierDOT representation X X X X *Y Y Y Y 3 2 1 03 2 1 0 X X XX X X 2 1 02 1 0 X2Y1X1Y1. Y Y Y x2 1YX X X Y Yx2 1 0X7* Y3Y2Y1Y0 06 5 4 X YX YX Y 2 01 00 0 X X X X *Y Y Y Y X Y 3 2 1 07 6 5 4 0 1 ...... X YX YX Y 2 21 20 2Y Y Y YX X X X * 7 6 5 47 6 5 4 R RR RR R 5 43 21 0 Computer Architectur e & Arithmetic Group3Stanford UniversityComputer Architectur e & Arithmetic Group4Stanford University
Generation of PPs Using ROMs
8 x 8 bit Multiply using 256x8b ROMs a b c d
4, 8, and 16 bit Multiply using 256x8bit ROMs 16x16 bit 8x8 bit 4x4 bit
n hCSA Delay 4 10 b 8 31 d a 16 74 c 32 156 64 318 Computer Architectur e & Arithmetic Group5Stanford University
Booths Algorithm Observation:We can replace a string of 1s in the multiplier by +1 and -1. . . . 0 1 1 1 1 1 0 . . . Example: . . . 0 1 1 1 1 1 0 . . . +1 - 1 . . . 1 0 0 0 0 0 0 . . . - 1 . . . 1 0 0 0 0-1 0 . . . X*(0 1 1 1 1 1)X*(1 0 0 0 0-1) Y Y X 1-X -1 X 10 0 X 10 0 X 10 0 X 10 0 0 0X 1
Computer Architectur e & Arithmetic Group6
Stanford University
EE 486
1
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