The Picard group
نویسنده
چکیده
Why should a number theorist be interested in algebraic geometry? In this course we hope to demonstrate one very good reason, by showing essentially geometric reasons why certain Diophantine equations fail to have solutions. But we will begin by placing the study of Diophantine equations into the context of algebraic geometry, to see how techniques from many different realms of mathematics can be useful in their study. Suppose that we are interested in studying the integer or rational solutions to a polynomial equation f ∈ Z[X0, X1, . . . , Xn]. We assume f to be homogeneous, so that the sets of rational and integer solutions concide: more precisely, any integer solution may be turned into a rational one by clearing denominators. We wish to define a geometric object X as
منابع مشابه
Solving fuzzy differential equations by using Picard method
In this paper, The Picard method is proposed to solve the system of first-order fuzzy differential equations $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.
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