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Jacobians of Genus One Curves
Abstract Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1, a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariantExpand
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A cup product in the Galois cohomology of number fields
This paper is devoted to the consideration of a certain cup product in the Galois cohomology of an algebraic number field with restricted ramification. Let n be a positive integer, let K be a numberExpand
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On the method of Coleman and Chabauty
Let C be a curve of genus g >_ 2, defined over a number field K , and let J be the Jacobian of C. Coleman [C2], following Chabauty, has shown how to obtain good bounds on the cardinality of C(K) ifExpand
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Duality theorems for néron models
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Critical care in the emergency department: A time‐based study
ObjectivesEmergency departments serve many functions in the current U.S. healthcare system, including initial management of patients with critical illnesses and primary care for a growing proportionExpand
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The Common Core State Standards in Mathematics
The Common Core State Standards in Mathematics were released in 2009 and have been adopted by 45 states. Expand
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Calculus: Single Variable
Chapter 1: A Library of Functions Chapter 2: Key Concept: The Derivative Chapter 3: Short-Cuts to Differentiation Chapter 4: Using the Derivative Chapter 5: Key Concept: The Definite Integral ChapterExpand
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Fish scale: an unusual foreign body.
Retained foreign bodies can be a source of infection and a cause of disability. A 63-year-old white man presented with a nonhealing wound of the right second finger of 1 month's duration. The injuryExpand
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