SFU

Thu 23 Oct 2014, 3:30pm
Number Theory Seminar
room ASB 10900 (SFU  IRMACS)

On Jacobians of dimension 2g that decompose into Jacobians of dimension g

room ASB 10900 (SFU  IRMACS)
Thu 23 Oct 2014, 3:30pm4:30pm
Abstract
Let X be a genus 2g curve defined over an arbitrary field of characteristic not equal to 2 and let J(X) the Jacobian variety of X. We say that a Jacobian variety is decomposable if it is isogenous to a product of abelian varieties. The type of decomposition can by characterized by the type of kernel of the isogeny and the dimensions of the varieties in the product. We consider isogenies with kernel type (Z/2Z)^{g} and products of dimension g Jacobian varieties. Additionally, we insist that the isogeny is polarized. In this talk we describe a family of (nonhyperelliptic) genus 2g curves whose Jacobians are decomposable in this way. We prove that all genus 4 curves whose Jacobian has this decomposition type are either in this family or arise from a different construction considered by Legendre. Joint work with Nils Bruin.
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Emory University

Thu 30 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126

Hasse principles over function fields of padic curves

room MATH 126
Thu 30 Oct 2014, 3:30pm4:30pm
Abstract
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UBC

Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126

TBA

room MATH 126
Thu 6 Nov 2014, 3:30pm4:30pm
Abstract
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Morningside Center of Mathematics and Purdue

Thu 13 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126

Introduction to Mochizuki's works on interuniversal Teichmuller theory

room MATH 126
Thu 13 Nov 2014, 3:30pm4:30pm
Abstract
Interuniversal Teichmuller theory, as developed by Mochizuki in the past decade, is an analogue for number fields of the classical Teichmuller theory, and also of the padic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to nonring theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in interuniversal Teichmuller theory. In this talk, we will try to give an introduction to these ideas.
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Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126


room MATH 126
Thu 20 Nov 2014, 3:30pm4:30pm
Abstract
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Oxford University

Thu 27 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126

TBA

room MATH 126
Thu 27 Nov 2014, 3:30pm4:30pm
Abstract
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