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MOTIVATION
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On Brumer-Stark Units and Hilbert’s 12th Problem by Mahesh Kakde and Samit Dasgupta
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- 1 A live interactive session with the speaker will be hosted online on February 23, 2022, at 06:00 PM Indian Standard Time. Viewers can send in their questions for the speaker in advance of the live in…
- 2 Start
- 3 Getting Started
- 4 Speakers
- 5 The Principle Aim & Format
- 6 Introduction
- 7 Preface
- 8 Diophantine Equations
- 9 Abelian extensions
- 10 Abelian extensions of imaginary quadratic fields
- 11 Hilbert's 12th problem
- 12 Stickelberger's theorem
- 13 Sickelberger's theorem
- 14 Analogue of Stickelberger's theorem for other number fields
- 15 General Stickelberger element
- 16 Brumer-Stark-Tate conjecture
- 17 Refinements of Brumer-Stark conjecture
- 18 Brumer-Stark-Tate from refinements
- 19 First reduction
- 20 MOTIVATION
- 21 EXPLICIT CLASS FIELD THEORY
- 22 THE BRUMER-STARK AND GROSS-STARK CONJECTURES
- 23 SOME OF MY PRIOR WORK IN THIS AREA
- 24 NEW RESULTS WITH MAHESH KAKDE
- 25 EXACT FORMULA FOR THE UNITS
- 26 COMPUTATIONAL EXAMPLE
- 27 A LARGER EXAMPLE
- 28 REFINEMENTS: CONJECTURES OF KURIHARA, BURNS, AND SANO
- 29 DEFINITION OF FITTING IDEAL
- 30 RITTER-WEISS MODULE
- 31 INCLUSION IMPLIES EQUALITY
- 32 RIBET'S METHOD
- 33 GROUP RING VALUED MODULAR FORMS
- 34 GROUP RING CUSP FORM
- 35 GALOIS REPRESENTATION
- 36 P-ADIC INTEGRAL FORMULA FOR UNITS
- 37 Thank you!
