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 Events
Avi Kulkarni
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, 3:30pm-4:30pm

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 (non-hyperelliptic) 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 p-adic curves
room MATH 126
Thu 30 Oct 2014, 3:30pm-4:30pm

Abstract

 
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Uriya First
UBC
Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
TBA
room MATH 126
Thu 6 Nov 2014, 3:30pm-4:30pm

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 inter-universal Teichmuller theory
room MATH 126
Thu 13 Nov 2014, 3:30pm-4:30pm

Abstract

Inter-universal 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 p-adic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to non-ring theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in inter-universal Teichmuller theory. In this talk, we will try to give an introduction to these ideas.
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TBA
Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
room MATH 126
Thu 20 Nov 2014, 3:30pm-4:30pm

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, 3:30pm-4:30pm

Abstract

 
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