کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4593180 | 1630647 | 2016 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Curvature on the integers, I
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
Starting with a symmetric/antisymmetric matrix with integer coefficients (which we view as an analogue of a metric/form on a principal bundle over the “manifold” SpecZ) we introduce arithmetic analogues of Chern connections and their curvature (in which usual partial derivative operators acting on functions are replaced by Fermat quotient operators acting on integer numbers); curvature is introduced via a formal patching technique. We prove various non-vanishing, respectively vanishing results for curvature; morally, SpecZ will appear as “intrinsically curved”. Along with [7], [8] and [9], this theory can be viewed as taking first steps in developing a “differential geometry of SpecZ”.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 167, October 2016, Pages 481–508
Journal: Journal of Number Theory - Volume 167, October 2016, Pages 481–508
نویسندگان
Malik Barrett, Alexandru Buium,