Rationality Problem for Algebraic Tori - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rationality Problem for Algebraic Tori write by Akinari Hoshi. This book was released on 2017. Rationality Problem for Algebraic Tori available in PDF, EPUB and Kindle. "We give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. We show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. We make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, we determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. We also show that the Krull-Schmidt theorem for G-lattices holds when the rank ≤ 4, and fails when the rank is 5. Indeed, there exist exactly 11 (resp. 131) G-lattices of rank 5 (resp. 6) which are decomposable into two different ranks. Moreover, when the rank is 6, there exist exactly 18 G-lattices which are decomposable into the same ranks but the direct summands are not isomorphic. We confirm that H1(G, F) = 0 for any Bravais group G of dimension n ≤ 6 where F is the flabby class of the corresponding G-lattice of rank n. In particular, H1(G, F) = 0 for any maximal finite subgroup G ≤ GL(n, Z) where n ≤ 6. As an application of the methods developed, some examples of not retract (stably) rational fields over k are given."--Page v.
Rationality Problem for Algebraic Tori
Rationality Problem for Algebraic Tori - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rationality Problem for Algebraic Tori write by Akinari Hoshi. This book was released on 2017-07-13. Rationality Problem for Algebraic Tori available in PDF, EPUB and Kindle. The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Rationality Problems in Algebraic Geometry
Rationality Problems in Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rationality Problems in Algebraic Geometry write by Arnaud Beauville. This book was released on 2016-12-06. Rationality Problems in Algebraic Geometry available in PDF, EPUB and Kindle. Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Multiplicative Invariant Fields of Dimension $leq 6$
Multiplicative Invariant Fields of Dimension $leq 6$ - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multiplicative Invariant Fields of Dimension $leq 6$ write by Akinari Hoshi. This book was released on 2023-03-09. Multiplicative Invariant Fields of Dimension $leq 6$ available in PDF, EPUB and Kindle. View the abstract.
Encyclopaedia of Mathematics
Encyclopaedia of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Encyclopaedia of Mathematics write by M. Hazewinkel. This book was released on 2013-12-01. Encyclopaedia of Mathematics available in PDF, EPUB and Kindle.
